U.S. patent number 4,136,530 [Application Number 05/770,316] was granted by the patent office on 1979-01-30 for rotary thermodynamic apparatus and method.
Invention is credited to Frederick W. Kantor.
United States Patent |
4,136,530 |
Kantor |
January 30, 1979 |
Rotary thermodynamic apparatus and method
Abstract
Rotary thermodynamic compression and refrigeration apparatus and
methods in which the mechanical impedance and/or thermodynamic
impedance of the system are controlled in order to obtain stable
operation. By controlling these impedances, the overall pressure
drop of the fluid flow in the system is made to increase with
increasing fluid flow rate, thus ensuring stable operation.
Inventors: |
Kantor; Frederick W. (New York,
NY) |
Family
ID: |
24275620 |
Appl.
No.: |
05/770,316 |
Filed: |
February 18, 1977 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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569478 |
Apr 18, 1975 |
4010018 |
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78552 |
Oct 6, 1970 |
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864112 |
Oct 6, 1969 |
3808828 |
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Current U.S.
Class: |
62/499;
165/183 |
Current CPC
Class: |
F25B
15/004 (20130101); F25B 3/00 (20130101); F04D
23/00 (20130101); Y02A 30/277 (20180101); Y02A
30/27 (20180101); Y02B 30/62 (20130101) |
Current International
Class: |
F04D
23/00 (20060101); F25B 15/00 (20060101); F25B
3/00 (20060101); F25B 003/00 () |
Field of
Search: |
;62/115,499
;165/179,183 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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418500 |
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Sep 1925 |
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DE2 |
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437009 |
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Oct 1935 |
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GB |
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Primary Examiner: Capossela; Ronald C.
Attorney, Agent or Firm: Curtis, Morris & Safford
Parent Case Text
This is a division of U.S. Pat. application Ser. No. 569,478, filed
Apr. 18, 1975, now U.S. Pat. No. 4,010,018 which is a continuation
of U.S. Pat. application Ser. No. 78,552, filed Oct. 6, 1970, now
abandoned which is a CIP of U.S. Ser. No. 864,112 filed Oct. 6,
1969 now U.S. Pat. No. 3,808,828.
Claims
I claim:
1. Thermodynamic heat pump apparatus comprising a rotary inertial
thermodynamic device comprising a conduit having a first section
extending away from a reference line and a second section extending
towards said reference line, means for pumping a fluid through said
conduit, means for rotating said conduit about said reference line,
means for extracting heat from the fluid in said first section and
conducting heat to the fluid in said second section, and impedance
control means for providing an increase in pressure drop for an
increase in flow rate of said fluid in said conduit.
2. Apparatus as in claim 1 in which said impedance control means
includes means for controlling the mechanical impedance to fluid
flow in said conduit.
3. Apparatus as in claim 1 in which said impedance control means
includes means for controlling the thermodynamic impedance of said
apparatus.
4. Apparatus as in claim 1 in which said impedance control means
includes a liquid trap.
5. Apparatus as in claim 1 in which said pumping means comprises a
rotary inertial thermodynamic compressor mounted to rotate with
said conduit.
6. A system as in claim 1 including a heat source for heating
working fluid in said rotary inertial thermodynamic device, said
impedance control means comprising means for giving said heat
source a relatively high thermodynamic impedance.
7. A system as in claim 6 in which said heat source comprises means
adapted to heat said working fluid primarily by radiation.
8. A system as in claim 7 including a vacuum environment for said
rotary inertial thermodynamic device.
9. A system as in claim 8 including an evacuated housing enclosing
said rotary inertial thermodynamic device.
10. A system as in claim 8 including vanes on said rotary inertial
thermodynamic device for radiative heat transport away therefrom,
stationary vanes interleaved therewith, a cooling fluid and means
for conducting said cooling fluid across a portion of said
stationary vanes to remove heat therefrom.
11. A system as in claim 7 in which said radiation is nuclear, and
said working fluid is absorptive to said radiation.
12. A heat pump as in claim 1 in which said conduit includes a
third section interconnecting said first and second sections
through said pumping means.
13. A heat pump as in claim 12 including flow-restricting
heat-exchangers in said first and second sections.
14. A heat pump as in claim 13 in which each of said
heat-exchangers comprises a plurality of small, parallel contiguous
tubes in said conduit.
Description
This invention relates to rotary thermodynamic apparatus and
methods. More specifically, this invention relates to means and
methods for stabilizing the operation of rotary inertial
thermodynamic apparatus.
A theoretically highly efficient but impractical refrigerator
device has been proposed in U.S. Pat. No. 2,393,338 to J. R.
Roebuck, and "A Novel Form of Refrigerator" 16 Journal of Applied
Physics 285 - 295, May, 1945 by J. R. Roebuck. The basic form of
the device proposed by Roebuck is shown in FIG. 1 of the drawings.
The tube 11, which is supported in bearings 10, is rotated at a
very high speed about central axis 1 in the direction indicated by
the arrow 12 by means of a drive motor (not shown).
Compressed air is introduced into tube 11 at its inlet 13. It
travels through section 2, parallel to the axis, through section 4
towards the axis, through section 5 parallel to the axis, and exits
at outlet 14. As the gas moves radially outward it is subjected to
centrifugal compressive forces. While moving in the section 3, the
gas is compressed and heated by the centrifugal force created by
the rotation of the tube 11. At least part of the heat of
compression is removed from the gas in section 3 by heat exchange
means (not shown) such as water flowing in cooling coils.
While moving in section 4, the gas expands, due to the reduction of
the distance of the gas from the axis 1 and the concomitant
reduction of the centrifugal force acting on the remaining mass of
gas between it and the axis, and the gas becomes substantially
cooler due to its expansion. The cooled gas then flows out of the
outlet opening 14 for use in refrigeration.
The system described above is one form of a "rotary inertial
thermodynamic system", as the latter expression is used herein, In
such a system is performed a "rotary inertial thermodynamic
method", as that expression is used herein. Other, greatly improved
forms of such a system and method are disclosed in my U.S. Pat. No.
3,470,704, issued Oct. 7, 1969, and my co-pending U.S. Pat.
application Ser. No. 864,112, filed Oct. 6, 1969 now U.S. Pat. No.
3,808,828. The disclosures of that patent and application hereby
are incorporated in this patent application by reference.
It is an object of the present invention to provide a rotary
inertial thermodynamic system and method in which the fluid flow is
stable. It is another object of the present invention to provide
such a system which is relatively compact, lightweight,
uncomplicated and inexpensive, and which is capable of operating
under a wide variety of conditions and in a wide variety of
environments.
In accordance with the present invention, the foregoing objects are
met by the provision of rotary inertial thermodynamic apparatus and
methods in which the flow is stabilized by controlling the
impedances to fluid flow in the system so that the overall pressure
drop of the fluid flow in the system is made to increase with an
increasing fluid flow rate.
The foregoing and other objects and advantages will be set forth in
or apparent from the following description and drawings.
In the drawings are included several graphs. It should be
understood that the graphs illustrate the relationships between the
variable qualitatively, and not quantitatively. In the
drawings:
FIG. 1 is a schematic drawing or a prior art device;
FIGS. 2 and 3 are graphs used in explaining some of the principles
of the present invention;
FIGS. 4 and 5 each show separate embodiments of the invention;
FIGS. 6 through 9 are graphs illustrating certain operational
features of the invention;
FIG. 10 shows, schematically, another embodiment of the
invention;
FIG. 11 is a graph illustrating operational principles of the
embodiment shown in FIG. 10;
FIG. 12 is a schematic perspective view of a preferred form of the
device shown in FIG. 10;
FIG. 13 is a cross-sectional view of the device shown in FIG.
12;
FIG. 14 is a schematic drawing of another embodiment of the present
invention;
FIGS. 15 and 16 are graphs illustrating the operation of the device
shown in FIG. 14;
FIG. 17 is a schematic drawing of another embodiment of the
invention;
FIGS. 18 through 21 are graphs depicting the operation of various
embodiments of the invention;
FIGS. 22, 23 and 24 each show a further embodiment of the
invention;
FIG. 25 is a graph depicting the operation of the device shown in
FIG. 24;
FIG. 26 is a schematic drawing of another embodiment of the
invention;
FIG. 27 is a graph depicting the operation of the device shown in
FIG. 26;
FIGS. 28 through 36 each show a separate embodiment of the
invention;
FIGS. 37 through 40 show various impedance control devices for the
invention;
FIGS. 41 through 52 and 54 each show another embodiment of the
invention;
FIGS. 53 and 55 are graphs illustrating operational features of the
devices shown in FIGS. 52 and 54, respectively;
FIGS. 56 through 58 show another embodiment of the invention;
FIGS. 59 through 64 each show another embodiment of the
invention;
FIGS. 65 and 66 show another embodiment;
FIGS. 67 and 68 show another embodiment;
FIG. 69 is an elevation, partly schematic view of another
embodiment of the invention;
FIG. 70 is a cross-sectional view taken along line 70--70 of FIG.
69;
FIG. 71 is a cross-sectional view taken along line 71--71 of FIG.
69;
FIG. 72 is a cross-sectional view taken along line 72--72 of FIG.
69;
FIGS. 73 and 74 each show another embodiment of the invention;
and
FIG. 75 is a schematic drawing illustrating certain operational
features of the invention.
GENERAL PRINCIPLES OF THE INVENTION
It will aid in the understanding of this invention to divide the
pressure drop in the fluid, as it flows through the rotating
conduit of a rotary inertial thermodynamic system, into a
"thermodynamic" component and "mechanical" component.
The "mechanical" pressure drop is caused by friction between the
fluid and the walls of the conduit it flows in. The mechanical
pressure drop increases with F, the fluid flow rate in the system.
FIG. 2 shows a curve .DELTA.P.sub.M which describes the typical
variation of mechanical pressure drop with flow rate in the device
of FIG. 1.
The mechanical pressure drop can be thought of as the pressure drop
due to the "mechanical impedance" to flow through the system.
The second component of total pressure drop is the "thermodynamic
pressure drop", .DELTA.P.sub.T. This component of the total
pressure drop is that caused by thermodynamic conditions of the
flow. One example of such a pressure drop is that caused by the
difference in the temperatures of the gas in the tube sections 3
and 4 in the device shown in FIG. 1. The gas in section 4 is cooler
and, therefore, denser than the gas in section 3. Therefore, the
back pressure created by centrifugal action on the gas in section 4
is greater than the forward pressure (i.e., pressure tending to
encourage flow in the direction indicated by the arrows in FIG. 1)
created by the same centrifugal action on the gas in section 3,
with the result that there is a net pressure drop due to this
temperature difference. Other examples of thermodynamic pressure
drops will be given below.
In FIG. 2, curve .DELTA.P.sub.T describes the typical variation of
the above-described type of thermodynamic pressure drop with F,
flow rate, for the device in FIG. 1. It can be seen that
.DELTA.P.sub.T decreases with increasing flow rate, and the curve
.DELTA.P.sub.T thus has a negative slope. The reason for this is
that as the flow rate increases, the amount of heat removed from
the gas flowing in tube section 3 decreases due to the fact that
there is a decreasing amount of time for the heat exchange means to
extract heat from each portion of gas passing through it. Thus, the
temperature difference between the gas in sections 3 and 4
decreases and the thermodynamic pressure drop decreases.
The thermodynamic pressure drop can be thought of as the pressure
drop caused by the "thermodynamic impedance" to fluid flow through
the system.
In order to calculate the mechanical and thermodynamic impedances
of the system, an operating point such as point 21 in FIG. 2 is
selected. Then tangents 22 and 23 to the curves are drawn. For
small fluctuations of flow rate or pressure drop near the operating
point 21, the thermodynamic flow impedance is proportional to the
slope of line 22, and the mechanical impedance is proportional to
the slope of line 23.
In accordance with one basic principle of the present invention, it
has been found that stability of the overall rotary inertial
thermodynamic system can be maintained if the total mechanical and
thermodynamic impedance of the system is positive (for small
fluctuations about an operating point); that is, if the total
pressure drop in the system increases with increasing flow rate.
This relationship is illustrated in FIg. 3. Curve 24 represents a
typical system with a total impedance characteristic which is
positive; i.e the pressure drop across the system increases with
increasing flow. Curve 25 represents a system having a total
pressure drop which is independent of flow rate. Curve 26
represents a system having a total pressure drop which decreases
with increasing flow. For a given flow rate, e.g., the rate at line
27, the following conditions exist.
The system represented by curve 24 can operate stably. Any
disturbance which tends to increase the flow gives rise to an
increasing pressure drop through the system, which tends to reduce
the flow. However, a system of the type described by curve 25 is
not stable. A small purturbation of its operation, which would tend
to increase the flow, does not give rise to a corresponding
increase in pressure drop to restore the system to its initial
condition. All decreasing curves, of which 26 is representative,
describe systems whose operation is unstable, i.e. any purturbation
of the system which tends to increase the flow gives rise to a
reduced pressure drop which, in turn, allows the flow to increase
further. There is no restorative mechanism to preserve the
operation of the system at a stable level or flow.
There are several ways in which the operation of a rotary inertial
thermodynamic system can be stabilized in accordance with the
above-stated principles. One of these is to increase the mechanical
impedance to flow, so that there is a composite impedance which has
a rising characteristic at the operating point, 27. Another
alternative, and one which can be more desirable from the
standpoint of efficiency and flexibility of operation, is to reduce
the thermodynamic impedance and its associated characteristic time
lag for the exchange of heat so that, again, the system has a
composite impedance displaying a rising characteristic curve, but
achieves this condition without sacrifice of flow capability or
mechanical efficiency.
MECHANICAL IMPEDANCE CONTROL
FIG. 4 illustrates two different mechanisms by means of which
stability of the system illustrated in FIG. 1 can be assured. Both
use the principle of increasing the relative mechanical impedance
so that it dominates the thermodynamic impedance, thus assuring a
positive total impedance.
The first way in which a high mechanical impedance might be
obtained is by using a stationary positive displacement pump 28 as
the gas compressor. Such a pump is, for example, a reciprocating
piston pump, a sliding vane pump, or any other pump offering high
impedance to the flow of gas to the system from the pump. Cold air
from the rotary portion of the system flows through refrigeration
apparatus (not shown) inluding heat exchange means using the cold
gas for cooling. Appropriate rotary seals are used to provide a
gas-tight coupling between the rotary and stationary portions of
the system. Relatively dense gases, such as "Freon 12" can be used
to reduce the required rotational speed of the device. The very
high impedance of the pump provides the positive impedance which
stabilizes the system. It should be pointed out that this means of
stabilization is not the preferred means, as will be more fully
explained below.
Another stabilizing means shown in FIG. 4 is the use of a heat
exchanger 29 of a form which restricts the gas flow in conduit 11
and thus adds a considerable amount of mechanical impedance to the
system, and, therefore, reduces the thermodynamic impedance
relative to he mechanical impedance and gives a positive total
impedance characteristic to the system. For example, the heat
exchanger 29 can be a porous, thermally conductive plug such as a
sintered metal plug; or one with a multiplicity of fine conduits.
Metal bodies with many tiny conduits can be formed by use of the
technology utilized in the production of grids for vacuum tubes by
extrusion of a composite body and subsequent etching of material
from this body to leave fine passages. Other exchanger structures
include very finely-formed fin structures produced by extrusion,
hobbing, or any of a wide variety of other techniques well known in
the art of constructing heat exchange devices, and in the art of
constructing mechanical damping devices to provide impedance to the
flow of a gas. Of course, the device 29 should function well as a
heat exchanger in order to efficiently remove the heat of
compression from the gas in section 3 of the tube 11.
A useful modification of the latter embodiment also is shown in
FIG. 4. In this modification, one or more additional conduit
sections 33 is connected in parallel with the first such section.
The sections preferably are added in opposed pairs in order to
maintain rotational balance of the rotary portion of the system. A
porpous plug 29 or similar restrictor is located in the
outwardly-extending section of each such parallel section. Thus,
each separate section contains its own stabilizing means. This has
the advantage of preventing unequal sharing of the fluid flow or
even reversal of flow in some sections, which well might occur if
the only stabilizing means were a single high-impedance external
pump 28. Additional plugs 30 can be inserted in the
inwardly-extending portions of the conduits to add further
stabilization.
SINGLE-STAGE IMPEDANCE-CONTROLLED THERMODYNAMIC COMPRESSOR
FIG. 5 illustrates the basic features of a compressor constructed
in accordance with the present invention. Thermodynamic compressors
of this type are described in my U.S. Pat. No. 3,470,704 and in my
copending application Ser. No. 864,112 now U.S. Pat. No. 3,808,828,
as utilized in a sealed, closed-circuit rotating thermodynamic
system to provide the actuating pressure to operate refrigeration
apparatus.
FIG. 6 is a graph showing the qualitative relationships between the
pressure P and temperature T of the gas in the compressor of FIG.
5. Referring to both FIGS. 5 and 6, a tube 52 like the tube 11 in
FIG. 1 is provided, and is rotated as in the FIG. 1 device. Gas
enters tube 52 at an inlet 53 at a pressure P.sub.17 and a
temperature T.sub.17. During the motion of this gas radially
outwardly through tube section 50, the pressure and temperature
increase essentially adiabatically to a new pressure and
temperature, P.sub.18, T.sub.18, corresponding to the pressure and
temperature at location 48 in FIG. 5. Then, the working fluid
returns towards the axis through tube section 51. In tube section
51 is located heat exchanger means 46, such as a porous plug, which
is provided to conduct heat from a source (not shown) in the
direction of arrow 61 into the working fluid to maintain the
working fluid at the temperature whihc it has reached during the
adiabatic compression and which it possessed at location 48. Due to
the heat exchanger 46, the expansion of the working fluid in part
of tube section 51 is essentially isothermal and is represented by
the isothermal decrease in pressure to P.sub.20, T.sub.18, shown in
FIG. 6. In the remainder of section 51, the pressure and
temperature drop to P.sub.19, T.sub.19. At each radial distance
from the axis of rotation 1 in FIG. 5, a volume element in tube
section 51 is at a higher temperature than a corresponding volume
element at a corresponding radial distance from axis 1 in tube
section 50. Therefore, the density in such a volume element in tube
51 is lower than that of its corresponding element in tube 50.
Centrifugal forces acting upon the column of gas extending radially
in tube section 51 exert a smaller total backward pressure than the
forward pressure exerted by centrifugal forces acting on the denser
column of gas in tube section 50. This gives rise to a net forward
driving pressure which drives gas through the system in the
direction indicated by arrow 54, i.e. P.sub.19 is greater than
P.sub.17. Also, T.sub.18 is greater than T.sub.17. Thus, this
device acts as a thermodynamic compressor which can be expected to
have high thermodynamic efficiency.
The same physical effects that give rise to a relationship between
thermodynamic pressure drop and flow rate for working fluid in a
refrigeration system of the type shown in FIG. 1, also give rise to
a pressure and flow relationship in the case of a compressor of the
type shown in FIG. 5. The compression arises from a difference in
temperature between gases in tube section 51 and tube section 50 in
FIG. 5. This temperature difference is maintained by a flow of heat
into the working fluid as indicated at 61. This flow of heat is not
instantaneous, that is, there is a characteristic time lag
associated with the process of heating the fluid. The faster the
flow of working fluid through the system, the less exposure time
the working fluid has in heat exchange means 46. This results in
less effective heat exchange and a smaller temperature difference
between the working fluid in tube section 51 and that in tube
section 50. Because of this, the thermodynamic pumping action of
this pump decreases with increasing flow rate. FIG. 7 shows the
relationship between the flow rate F and the pumping pressure
.DELTA.P.sub.T produced by the compressor shown in FIG. 5. The
above-described behavior is indicated generally in FIG. 7 by curve
portion 101, which represents a decrease in thermodynamic pumping
pressure with increase in flow.
For the purpose of explanation, suppose that we were to force
working fluid backwards through this pump against the pressure
gradient maintained by the thermodynamic pumping action. In that
case, the working fluid would be flowing in the direction opposite
to that indicated by arrow 54 in FIG. 5. The first consequence of
this reversal in direction of flow is that the portion of tube
section 51 which is located between heat exchanger 46 and the axis
1 no longer contains heated working fluid. The working fluid heated
by heat exchanger 46 is carried radially outwardly and returns
towards the axis 1 in tube section 50. Tube section 50 thus
contains heated working fluid. The region 48 of the tube 52, which
is located further from the axis 1 than the radius 63 of the
radially outermost point of heat exchanger 46, can be regarded as
an adiabatic region containing heated working fluid whose
temperature and pressure depend only upon the radial distance of
the point at which temperature and pressure are measured from the
axis of rotation 1. The working fluid returns to axis 1 in tube
section 50, and its expansion therein can be regarded as
essentially adiabatic. In the tube section 65, between radial
distance 63 and the axis 1, the temperature of the working fluid in
tube section 50 is greater than the temperature of the working
fluid in tube section 51 at corresponding radial location. For this
reason, the working fluid in tube section 65, when acted upon by
contrifugal forces, exerts a smaller pressure in the direction
indicated by arrow 54 than does the corresponding body of working
fluid in tube section 51, in the direction opposite to the arrow
54. For this reason, there is a net pumping action in the reverse
direction. This is depicted graphically in FIG. 7 by curve segment
102. As the flow rate in the reverse direction is increased, the
working fluid passing through heat exchanger 46 interacts less
efficiently with it. One consequence of this is that the working
fluid reaches its maximum temperature just at the point where it
leaves the heat exchanger. For this reason, the working fluid in
tube section 65, at those radii corresponding to locations within
tube section 51 occupied by heat exchanger 46, has a higher
temperature than does the working fluid within the heat exchanger
itself. For this reason, it is possible for the pumping action to
increase for working fluid flowing more quickly in the reverse
direction. If the flow of the working fluid backwards is made very
great, the effect of heat exchanger 46, in changing the temperature
of the working fluid passing through the system, becomes
essentially negligible. In that case, there is no physical effect
of temperature difference, and the thermodynamic pumping pressure
differential goes asymptotically to zero for large flows.
The most pronounced feature illustrated by FIG. 7 is that the
thermodynamic pumping mechanisn can work to pump working fluid in
either the positive flow direction or the negative flow direction.
There is a narrow region within which the pressure of the
thermodynamic pumping action in the two different directions is
joined, here designated by dashed curve segment 103. The details of
the form of curve segment 103 depend upon the details of heat
exchange and convection and are profoundly affected by the geometry
of the device. However, essentially none of the possible variations
of the geometry can stabilize the system at the zero flow point.
Note that the pumping effect is an increase in pressure at the
output compared to the pressure at the intake for the pumping
system. For this reason, it has a negative sign, compared to a
mechanical resistance to flow, and is designated in FIG. 7 by -
.DELTA.P.sub.T.
FIG. 8 illustrates the relationship between the flow rate F and the
mechanical pressure drop .DELTA.P.sub.M in the device of FIG. 5.
Mechanical resistance to flow always opposes the flow, i.e. for a
positive flow there is a positive drop in pressure, taking the
inlet pressure minus the outlet pressure. Using that convention,
for a positive flow there is a positive .DELTA.P.sub.M, and for a
negative flow a negative .DELTA.P.sub.M. This is indicated
schematically by curve 104 in FIG. 8. Note that in the region near
zero flow rate where there is the greatest problem in stabilizing
the thermodynamic compression mechanism, the effect of the
mechanical impedance to flow is the least.
The overall performance of a single pumping loop of the type
illustrated in FIG. 5 is represented graphically in FIG. 9.
.DELTA.P in FIG. 9 is the total pressure difference, defined as
pressure at inlet 53 minus pressure at outlet 49, for compressor 52
in FIG. 5. .DELTA.P is defined as the algebreic sum of the
mechanical pressure and the thermodynamic pressure differences,
observing the sign convention defined above. Curve portion 105 in
FIG. 9 represents flow in the forward direction, and portion 106
represents flow in the reverse direction. The curve portion in the
fourth quadrant represents operation of the system as a compressor,
driving its own flow in the forward direction. The region in the
second quadrant represents the compressor driving its own flow in
the reverse direction. .DELTA.P, for small reverse flow, is
represented very approximately by dashed curve portion 108. The
intersection of a line 107 and line 105 is a selected operating
point Q, with flow F.sub.Q and compression C.sub.Q. The following
equation expresses the relationship between C and F: C =
-.DELTA.P(F), when .DELTA.P(F) is a function of the flow F. Line
109 is tangent to curve 105 at the operating point Q, and the slope
of line 109, for small fluctuations of flow near point Q, gives a
measure of the rate of change of .DELTA.P with F. It can be seen
that the tangent line 109 is positive. Thus, the compression C
which serves to drive the flow F in the forward direction decreases
with increasing flow. For this reason, operation of the system at
the selected operating point Q, is stable with respect to small
fluctuations in flow. A fluctuation tending to increase the flow
decreases the driving compression available to continue the flow.
This allows the flow to return to its original value. Similarly, a
fluctuation which tends to decrease the flow increases the amount
of compression available to drive the flow, which in turn restores
the flow to its original value. It is important to select the
operating point Q far enough from the zero flow point so that
fluctuations in the temperatures and pressures of operation of the
system will not produce an excursion in the flow rate sufficient to
take the flow from its selected operating point through the zero
value and force the system into operation in a reverse flow
mode.
One of the most important single aspects of the operation of a
rotary inertial thermodynamic compressor of the kind shown in FIG.
5 is that stable operation requires that the forward flow be
substantially different from zero. Thus, stable operation of the
compressor requires that the external impedance not be so large in
relation to the internal impedances of the compressor as to reduce
the flow to such a small level that the fluctuations in the
pressure generated by the compressor or in the pressure reflected
by the external load would force the flow of working fluid to
reverse, even briefly.
CASCADE IMPEDANCE CONTROLLED THERMODYNAMIC COMPRESSOR
FIG. 10 shows, schematically, a compressor 199 in which several
single-loop compressors of the type shown in FIG. 5 are connected
together in series ("cascaded") in order to provide an increase in
compression over that available from a single loop. Such a cascaded
compressor is particularly desirable in uses in which it is not
possible, because of limitations on input and output temperature,
rotational speed, size of the device, or because of the nature of
the working fluid, to achieve the desired compression with stable
operation in a single loop. The compressor 199 includes a conduit
200 which has three U-shaped loops. At appropriate places within
the conduit 200 are located heat exchangers, e.g., porous plugs,
133, 135, 137, 139, and 141. Working fluid (gas) enters the system
at inlet 131 and travels radially outward through conduit section
132, experiencing essentially adiabatic compression. It returns
towards axis 1 in conduit section 134, passing first through heat
exchanger 133 within which it experiences expansion, which can be
regarded as essentially isothermal. The working fluid then
continues towards axis 1 through region 144 of conduit section 134,
within which its continued expansion as it approaches axis 1 is
essentially adiabatic. In moving from inlet 131 to station 201,
located on the rotational axis 1, the working fluid has passed
through a rotary thermodynamic compressor stage essentially like
that described in FIG. 5. In FIG. 10 this first stage of
compression is given reference numeral 202. Second and third stages
203 and 204 follow stage 202.
The second stage 203 includes conduit sections 136 and 138, and
heat exchange means 135 and 137. Working fluid continues from
station 201 through heat exchange means 135, moving radially
outwardly. Within heat exchange means 135 the compression of the
working fluid can be regarded as essentially isothermal, i.e. the
heat exchanger 135 allows heat of compression to leave the working
fluid during compression. After passing through heat exchange means
135, the working fluid continues through the region 145 beyond heat
exchanger 135, within which its compression, as it moves radially
outward, is essentially adiabatic. The working fluid then returns
to axis 1 through heat exchanger 137, within which its expansion on
returning towards the axis is essentially isothermal, and then
through conduit region 146, within which its further expansion is
essentially adiabatic.
The working fluid next flows through the third stage 204, in which
it is acted upon in substantially the same manner as in the second
stage 203. The compressed gas emerges from an outlet opening
143.
It should be understood that heat is added to the working fluid
from one or more heat sources through each of the heat exchangers
133, 137 and 141 so as to maintain the flow through those
exchangers essentially isothermal.
FIG. 11 shows the relationships which are believed to exist between
the pressure and temperature of the working fluid as it passes
through compressor 199 shown in FIG. 10. Point 149 represents the
pressure and temperature of the working fluid at the inlet 131.
Line segment 150 describes the adiabatic compression of the working
fluid in conduit section 132. Line segment 152 describes the
isothermal expansion of working fluid returning towards axis 1 in
heat exchanger 133. Line segment 154 describes the adiabatic
expansion of working fluid within region 144 of conduit section
134. The point 155 gives the pressure and temperature of the
working fluid at station 201 in FIG. 19. This is its temperature
and pressure after having completed passage through the first
compressor stage 202. The arrows next to the various portions of
the curve in FIG. 11 indicate the progress of a volume element of
working fluid through the compressor 199.
The difference in pressure between points 155 and 149, designated
C.sub.1, represents the compression provided by the first stage 202
of compression.
In the second stage of compression, line segment 156 designates the
isothermal compression of working fluid within heat exchanger 135.
Line segment 157 represents the adiabatic compression of working
fluid within region 145 of conduit segment 136. Line segment 159
represents the isothermal expansion of working fluid within heat
exchange means 137 in conduit segment 138. Line segment 160
represents the essentially adiabatic further expansion of working
fluid in region 146 of conduit section 138. Point 170 represents
the pressure and temperature at station 205. This completes the
second stage of compression 203, and the compression provided by
this second stage is designated C.sub.2 in FIG. 11.
Compression stage 204 is represented by line segments 171, 172, 173
and 174, corresponding respectively to isothermal compression
within heat exchange means 139 of conduit segment 140, adiabatic
compression within region 147 of conduit 140, isothermal expansion
within heat exchange means 141 of conduit segment 152 and adiabatic
expansion in region 148 of conduit segment 152. Point 161 in FIG.
11 represents the pressure and temperature of the working fluid at
outlet 143 of the compressor 199. The difference in pressure
between point 161 and point 170, designated C.sub.3 in FIG. 11, is
the compression occurring within the third stage 204 of the
compressor. The total compression provided by the entire compressor
is represented by the difference in pressure between point 161 and
point 149 (the sum of C.sub.1, C.sub.2 and C.sub.3), and is
designated in FIG. 11 by C.
The provision of adiabatic compression in the first section 132 of
the compressor 199 is optional. If desired or necessary, a heat
exchanger positioned like heat exchangers 135 and 139 can be used
to make the compression isothermal. Ordinarily, however, the gas
entering the compressor will be cool and isothermal compression in
the first stage will be unnecessary.
Except for the above-described optional feature of the first stage
of the compressor 199, all of the stages preferably are essentially
identical to one another.
There is another, perhaps simpler, way to analyze the behavior of
the cascaded compressor 199. The compression produced by a rotary
thermodynamic compressor of the form illustrated in FIG. 5, depends
upon the input pressure for the device, assuming that all other
operating parameters are held constant. This approximation applies
to the case where the flow of working fluid through system is not
so great as to render heat exchange within the heat exchange means
relatively ineffective. This proportionality between the
compression in a single stage and the input pressure to that stage
is a consequence of the production of pressure by the action of
centrifugal forces on the columns of gas within tube sections 65
and 62 in FIG. 5. The total pressure in the forward direction, as
designated by arrow 54, produced by the column of gas in tube
section 65 depends upon the centrifugal force acting upon the mass
of gas in that tube section. The reverse pressure produced by
working fluid in tube section 62, trying to force working fluid
against the direction indicated by arrow 54, also depends upon the
action of centrifugal forces on the mass of the working fluid
present within column 62. The difference in density between the
working fluid in the two columns, 65 and 62, is a consequence of a
difference in temperature within those two columns. For an ideal
gas the ratio of the density in one column 65 to the density in the
other column 62 depends upon the ratio of the temperatures. For a
fixed relationship in temperatures the absolute difference in
density between the working fluid in the two columns is
proportional the the absolute density of the working fluid. This
density, in turn, depends upon the overall pressure of the working
fluid within the system, and, for relatively small flow rates, is
explicitly a single-valued function of the pressure at the inlet to
the compression stage. Thus, for an ideal gas, the absolute
difference in pressure produced by the operation of a single-stage
of a rotary thermodynamic compressor is proportional to the
pressure at its inlet. This behavior for a cascaded compressor is
illustrated in FIG. 11. The pressure difference C.sub.2 produced in
the second stage of compression, is not as large as the pressure
difference C.sub.3 produced in the third stage. This is because the
inlet pressure at the intake to the second stage of compression is
not as high as the inlet pressure at the third state. In FIG. 11,
operation is assumed to be with a working fluid which is an ideal
gas, and the pressure increment for each stage of compression after
the first stage is roughly proportional to the inlet pressure for
that stage. One consequence of this physical effect is that
operation of a rotary thermodynamic compressor with many stages can
be characterized as a multiplication of the inlet pressure by a
ratio, which, for flows not so large as to render the operation of
the heat exchange means within the system relatively ineffective,
nor so large as to cause appreciable friction, is independent of
both inlet pressure and flow. This leads to an exponential
dependence of the form shown in the following equation:
in which P.sub.out is the outlet pressure, P.sub.in is the inlet
pressure, R.sub.p is the compression ratio for each stage and N is
the number of stages in cascade.
Cascading rotary thermodynamic compressors of this form is a way to
achieve capability of delivering working fluid at a higher pressure
than would otherwise be possible. This increases the resistance to
reverse flow through the compressor, and thus increases the
impedance of a load to which such a compressor system can stably
deliver working fluid. Moreover, because the output pressure
increases exponentially with the number of cascaded stages,
cascading the stages results in a greater total impedance than the
sum of the individual impedances of each stage operating alone, and
thus stabilizes the compressor substantially more effectively than
might be considered to be possible.
One modification of the compressor 199 can be formed by using
several parallel branches, each of which contains several stages in
cascade, in order to deliver a larger volume of working fluid, and
in order to provide flexibility in the geometric arrangement of the
various pumping stages within the device. For instance, such
parallel branches can be used to provide for dynamic balance of the
system when it is working into various gas pressure loads.
HELICAL-TOROIDAL THERMODYNAMIC COMPRESSOR
FIGS. 12 and 13 show a cascaded multi-stage thermodynamic
compressor 500 with stages like those shown in FIG. 10, but
arranged in a particularly advantageous formation.
As is shown schematically in FIG. 12, the compressor 500 includes
two groups of loops 510 and 512 of tubing. Each group of loops is
formed by winding a single length of tubing in a pattern tending to
form a toroid. Each loop 510 is opposite to a loop 512 in the
opposite group, and the loops are arranged symmetrically with
respect to the central axis 517 of the toroid.
The starting end of the upper group of loops 510 is connected to
the starting end of the opposite group 512. This connection is
indicated by reference numeral 516. Similarly, the trailing ends of
the groups are connected together as indicated at 518. Thus, the
two groups are connected together in parallel. A refrigeration unit
or other load 519 is connected to the conduits 516 and 518. The
refrigeration unit 519 contains, for example, means of the type
described above for centrifugally compressing, expanding and
returning a working fluid to the compressor 500 through the conduit
516. The compressor 500 and the refrigeration unit 519 are
connected together to be rotated as a rotary heat pump unit by a
motor 504.
As is shown in FIG. 13, the loops 510 and 512 are secured between a
pair of heat-conducting metal plates 506 and 508 by means of
welding or soldering. The plates 506 and 508 are secured to a
hollow shaft 502 through the center of which pass tubes 516 and
518. Insulation 514 fills the toroidal hole formed by the loops 510
and 512. The plates 506 and 508 may have suitable heat transfer
fins on their outer surfaces.
The various compression stages are arranged so that all of the heat
exchangers 135, 139, etc., through which heat is rejected contact
the plate 508. Heat is conducted into plate 506 from the working
fluid, and is dissipated from plate 508 into the environment.
Similarly, heat exchange means 133, 137 and 141, through which heat
is absorbed into the working fluid during expansion, make thermal
contact with the plate 506 through which heat flows into the
working fluid.
The compressor 500 operates as follows: Heat is added to the
portions of the loops in which the working fluid flows towards the
axis 517 by heating the plate 506, and the portions of the loops in
which the fluid flows away from the axis 517 are cooled by cooling
the plate 508. Rotation of the loops augments the pressure
difference between the outwardly and inwardly flowing fluid columns
in each loop in the manner discussed above. Since the loops in each
group are connected together in series, the compression produced by
each loop multiplies that produced by the preceeding loops in the
group, with the result that relatively high total fluid pressures
can be produced with working fluids of relatively low density, or
with the use of relatively low rotational speeds, or with rotary
devices having relatively small diameters. Alternatively, rather
than using this embodiment of the invention to reduce the foregoing
parameters, it can be used simply to produce very high total fluid
pressures.
The arrangement of the loops into two parallel-connected groups is
made in order to ensure that opposite portions of the rotary
structure will have the same amounts of fluid in them at the same
time and the rotational balance of the structure will be
maintained. Additional parallel-connected groups can be added as
desired.
EXTERNAL IMPEDANCES
All of the rotary thermodynamic devices discussed so far have in
common the same physical principle of operation. This is true
independent of whether the system is used for cooling or for
compression, whether the system has a single branch through which
fluid can pass or multiple branches in parallel, whether the system
has a single stage or a series of cascaded stages, whether the
system is part of a closed rotating loop, or is open in the sense
that working fluid enters and leaves the rotating assembly. The
principle of operation which all of these devices have in common is
the interaction within a rotating system of inertial forces which
arise within the rotating system and the thermodynamic properties
of a working fluid. These inertial forces are known as centrifugal
forces and coriolis forces. The centrifugal forces are the familiar
forces which tend to throw material out toward the rim of a
spinning chamber. The coriolis forces are those which act upon
material moving outwardly in a duct to bring it up to speed so that
its tangential velocity about the axis matches that of the channel
within which it is moving. Similarly, when material is moving from
near the periphery to near the axis, coriolis forces act to slow
down the material so that when it reaches the axis its tangential
velocity has been reduced from that which it had near the
periphery. It is the interaction of these rotary inertial forces
with differences in density of the working fluid, associated with
differences in temperature, which link thermodynamic work in the
form of the flow of heat to thermodynamic work in the form of flow
of a pressurized working fluid within these systems. It is this
relationship between thermodynamic flows of heat and mechanical
flows of working fluid which gives rise to the characteristic
dynamic properties discussed above. The dynamic instabilities which
have been discussed are, therefore, a characteristic property of
rotary inertial thermodynamic devices. These instabilities arise
when there is an improper relationship between the thermodynamic
impedances and mechanical impedances for the various parts of the
thermodynamic device and the other parts of the system, of which it
is a component. The mechanical impedance to the flow of working
fluid within a rotary inertial thermodynamic device may be regarded
as a property of the device itself and the external flow impedance
to which it is coupled. The thermodynamic impedances presented to
working fluid within the system include both the thermodynamic
impedances for exchange of heat within the device itself and also
the thermodynamic impedances external to the flow of the working
fluid proper. All of these thermodynamic impedances should be
considered in determining the stability of flow of working fluid
within the rotary inertial thermodynamic device.
For example, suppose that the cooling device diagrammed in FIG. 4
had in tube section 3 a very efficient heat exchange means for
allowing heat to flow from the working fluid during its compression
into the heat exchange means itself. Suppose, however, that this
heat exchange means was only relatively ineffectually linked to an
external sink to which the heat could be dissipated. The ability of
the heat exchange means to remove heat from the working fluid
during compression would then depend, not only upon the
effectiveness with which the heat in the working fluid could be
exchanged with the heat exchange means itself, but also upon the
effectiveness with which this heat exchange means could dissipate
the heat to some other part of the system. This total thermodynamic
impedance is what characterizes the thermodynamic impedance
presented to the working fluid. If this total thermodynamic
impedance is very high, even if there is only a relatively small
flow, the system will not be capable of dissipating the heat of
compression from the working fluid and will have a rapid drop in
the back-pressure by which it acts to use the pressure of the
working fluid entering the system to produce cooling. If, on the
other hand, the total thermodynamic immpedance with respect to the
working fluid in tube section 3 is very small, even when there is a
relatively large flow of working fluid a cooling effect can be
expected.
HEAT SOURCE IMPEDANCES
The characteristic thermodynamic impedance of the heat source is
another impedance of the system which should be taken into
consideration in stabilizing a rotary inertial thermodynamic
system. The impedance of a heat source is analogous, in some
respects, to the internal impedance of a source of electrical
energy.
In this analogy, heat flow corresponds to electrical current, and
temperature corresponds to voltage. Thus, a high-impedance heat
source is one in which the heat flow is relatively constant
regardless of the temperature of the medium into which it delivers
heat. Conversely, a low-impedance heat source is one in which the
temperature is relatively constant regardless of the amount of heat
flow in to the medium. Hence, a high-impedance heat source is
analogous to a constant-current electrical source, and a
low-impedance heat source is analogous to a constant-voltage
electrical source.
Examples of high-impedance heat source are flames and hot air. An
example of a low-impedance heat source is a relatively large body
of hot water. Other examples of both types of heat sources will be
given below.
As an example of the influence of the impedance of the heat source
on the stability of a rotary inertial thermodynamic device,
consider the device shown in FIG. 5. The heat exchange means 46 in
the tube section 62 is coupled to an external source of heat which
has, of course, a characteristic thermodynamic impedance. If the
impedance of the heat source is very high, as the flow rate of
working fluid through the compressor 52 decreases because of an
increasing back-pressure against which the system must deliver
working fluid, the amount of flow of working fluid past heat
exchange means 46 available to take heat away from it decreases,
and, therefore, the temperature of heat exchange means 46
increases. The result of this increase in temperature of heat
exchange means 46 is that the density of working fluid in the tube
section 62 decreases, increasing the effective compression
available from the rotary inertial thermodynamic system. Thus, the
use of a heat source with high thermodynamic impedance tends to
stabilize the operation of the compressor in the presence of large
back pressures from external loads in that the higher compression
enables the device to better resist reversal of flow from the load
back through the compressor.
IMPEDANCE-STABILIZED CLOSED-LOOP ROTARY INERTIAL HEAT PUMP
the principles discussed in the preceeding section can be utilized
to ensure the stable operation of a wide variety of rotary inertial
thermodynamic systems, including a closed-loop rotary inertial
thermodynamic system 300 of the form described in my U.S. Pat. No.
3,470,704 and shown schematically in FIG. 14. The device 300 has a
compressor section 311, and a cooling section 312. The compressor
section includes conduit sections 301 and 302, heat exchange means
303, and an expansion region 304 within conduit section 302.
Compressor 311 is a rotary inertial thermodynamic compressor. The
cooler section 312 includes conduit segments 305 and 308, and heat
exchangers 306 and 309. Heat exchangers 306 and 309 extend for a
substantially the full lengths of conduit sections 305 and 308.
Cooler 312 is a rotary inertial thermodynamic cooler. Conduit
section 310 completes the closed loop conduit.
The operation of rotary inertial thermodynamic compressor 311 is
characterized by FIG. 15 which is a graph relating the change in
pressure in the compressor and the cooler to the rate of flow of
working fluid through the system. Note the sign convention for
pressure change, which leads to a representation of P of the
compressor being negative, i.e., the drop in pressure of working
fluid flowing through it is negative; the pressure produced is
positive.
The properties of the cooler 312 are represented by curve 313 in
FIG. 15. It can be seen that P for the cooler decreases at first
with increasing flow, as the thermodynamic back-pressure decreases.
At relatively high flow rates, mechanical impedances dominate and
the pressure drop through the system again rises. Note that the
rate of drop curve 313 in FIG. 15, representing the back-pressure
generated in the cooler, is a consequence of a loss of heat from
the working fluid during compression in tube section 305 by means
of heat exchange means 306, and the gaining of heat from the
environment during expansion of the working fluid in tube section
308 by means of heat exchange means 309.
If the thermodynamic coupling of heat exchange means 306 and 309 to
their environments is very poor, then the rate of drop of the
back-pressure generated in cooler 312 would be much steeper than
that shown in curve 313. The relationship of back-pressure to flow
for this condition is represented by dashed curve 315 in FIG.
15.
FIG. 16 shows a curve 317 relating the total pressure drop through
both the compressor 311 and the cooler 312, acting in series, to
flow rate F. Stable operation of the system as a closed loop occurs
when the total pressure drop in going around the loop is zero, and
the slope dP/dF is positive. Curve 317 passes through zero total
pressure drop at an operating point 316. Flow in the system at
point 316 is stable and efficient. Limitations on the flow of the
working fluid arise primarily from thermodynamic effects, rather
than from mechanical, frictional constraints.
Curve 318 in FIG. 16 represents the total pressure drop in
compressor 311 and cooler 312 in the case in which cooler 312 has
only very little thermodynamic coupling to its environment. That
is, curve 318 represents total pressure drop for the same
conditions represented by curve 315 of FIG. 15. Curve 318
represents the algebraic sum of curves 315 and 314. Curve 318
crosses the zero axis at an operating point 319. This point
represents a condition in which the working fluid is circulating
very rapidly through the system and the amount of work done by the
working fluid against the thermodynamic pressure drop within cooler
312 is very small. The principal limitations on the flow are caused
by friction.
The efficient operation of the rotary inertial thermodynamic device
300 as a heat-actuated cooling system requires that the flow of
working fluid within the device be limited principally by
thermodynamic effects rather than by mechanical friction of the
working fluid within the conduits and heat exchangers through which
it passes. The reason for this is that the mechanical friction on
the working fluid is an irreversible thermodynamic loss. Thus, to
achieve stable, efficient operation of the device 300, it is
desirable that the cooler 312, regarded as a total system
(including those parts of its environment with which it exchanges
heat) present a lower thermodynamic impedance than is presented by
the compressor 311, regarded as a total system (including those
parts of its environment with which it exchanges heat). If the
foregoing constraints on thermodynamic impedance cannot readily be
met, the operation of the systemm can be stabilized by inclusion,
anywhere within the conduit, of a flow restricting means 320 (FIG.
14), for instance a constriction or a porous plug in the conduit.
This flow restrictor can advantageously be combined with one of the
various heat exchange means present within the conduit, although it
is not necessary to make such a combination.
As a second example, consider the problem of the stability of an
"open loop" rotary inertial thermodynamic system; e.g., a system of
the type shown in FIG. 4 in which a stationary source of working
fluid is used. A parallel-branch embodiment 349 of such a system is
shown schematically in FIG. 17, in which 360 is the inlet, and 361
is the outlet. The device has four branches 350, 351, 352 and 353,
containing, respectively, compression sections 348, 357, 358 and
359, which contain, respectively, heat exhangers 347, 354, 355 and
356. These heat exchange means are coupled to an external
environment, into which they can reject the heat of compression
which they receive from the working fluid as it is compressed.
FIG. 18 shows a curve 362 relating the frictional (mechanical)
pressure drop of working fluid in passing through one of the
branches (which are assumed to be identical) to the flow F or
working fluid through that branch, and a curve 363 relating the
thermodynamic pressure drop to the same flow. In FIG. 19 the curve
364 relates the total pressure drop within each branch to flow.
Curve 364 is the algebraic sum of curves 362 and 363 in FIG. 18. An
operating point 365 is selected at the point of tangency of a
tangent line 366 which has a positive slope.
By making the mechanical impedance in each one of the branches
sufficiently large, the pressure drop within that branch can be
dominated by the mechanical impedance, rather than by the
thermodynamic impedance. In this way, it is possible to select an
operating point where the curve 364 has a positive slope, i.e., a
small increase in the flow through that branch would be accompanied
by an increase in the pressure drop within the branch. This means
that the flow through the branch would decrease. Similarly, any
decrease in the flow through that branch would lead to a decrease
in the pressure drop, thus allowing the flow to increase.
Therefore, the flow at the operating point 365 is stable.
The mechanical impedance can be simply the impedance of the heat
exchanger in that branch. Separate flow restrictors also can be
used. The high mechanical impedance necessary for stability causes
irreversible thermodynamic losses. For this reason, although the
multiple-branch cooler 349 shown in FIG. 17 might appear
attractive, a detailed analysis, including an analysis of possible
dynamic instabilities, shows that its thermodynamic efficiency is
not nearly as high as in alternative embodiments disclosed
herein.
The length and positions of the heat exchangers inn the conduits is
a factor to be consideredd in the construction of rotary inertial
thermodynamic devices. Consider the case where the rotary inertial
thermodynamic device in FIG. 4 is operated as a single-branch
compressor of the type in FIG. 5 with heat supplied to heat
exchange means 30. Consider first the case where heat exchangers 29
and 30 are relatively short, and exchanger 29 is placed near the
axis 1, and exchanger 30 is remote from the axis. For this
discussion, it is assumed that fluid in the rest of the system is
relatively cool. Assume also that flow is opposite to the arrow 31.
This causes region 4 to be filled with cool working fluid, and
region 32 to be filled with the working fluid which has been heated
by its passage through heat exchanger 30. The result is that, even
for small reverse flows (in a direction opposite to arrow 31), the
system ceases to operate as a compressor driving working fluid in
the forward direction and begins to drive working fluid in the
reverse direction.
FIG. 20 is a graph illustrating the operation as a compressor of
the device shown in FIG. 4 with varying lengths of the heat
exchangers 29 and 30. Frictional effects are included. Curve 409
represents flow in the forward direction indicated by arrow 31.
Curve 412 represents reverse flow with short heat exchangers
positioned as described above. Curve 411 represents conditions
identical of those of curve 412, except that the heat exchangers
are longer, and curve 410 represents the case in which the
exchangers are so long that they substantially fill the tube
sections in which they are located.
The change from forward to reverse flow results in a sudden change
G.sub.1 or G.sub.2 in the compression available. As the heat
exchangers are elongated to fill progressively larger portions of
the conduit segments, the effect produced by changing the
temperature of the working fluid in sections 32 and 4 becomes
smaller. For small flows, it is assumed that the working fluid
within heat exchangers is essentially the temperature of the heat
exchanger. Therefore, the change in pressure appearing for small
flows in the reverse direction is reduced by extending the length
of these heat exchangers. Thus, with the longest heat exchangers,
the change in pressure appearing upon reversal of flow through the
system is essentially zero. However, extending the length of the
heat exchangers beyond the length required to produce the
isothermal compression and expansion required for operation in the
Carnot cycle reduces the efficiency of the system. This is because
the region 32 for adiabatic compression and the region 4 for
adiabatic expansion become very small. This does not allow adequate
compression to occur in section 32 to allow the working fluid to
achieve at station 15 a temperature equal to that of heat exchanger
30. In the case of reduction of length of adiabatic region 4, the
result is that working fluid leaving the system through outlet 34
is at a higher temperature because it has had less adiabatic
expansion to reduce its temperature from that which it possessed
upon leaving heat exchanger 30. The result is that the
thermodynamic efficiency of the system is decreased at the same
time that the gap in pressure upon small reversal of flow of
working fluid through the system is decreased.
Dashed curve 417 in FIG. 20 represents pressure variations with
small flows in the forward direction in a device as shown in FIG. 4
used as a commpressor in which the heat exchange means has a
relatively high thermodynamic impedance to the flow of heat from
the external heat source into the working fluid. This high
thermodynamic impedance can be caused either by the high internal
impedance of the source itself, or a high thermodynamic impedance
to the flow of heat into the working fluid, or by both. The result
of this high impedance is that, for smmall flows of working fluid
forward through the compressing system, the temperature of heat
exchanger 30 increases so that the amount of compression available,
due to the difference in density of the fluid in the outwardly and
inwardly directed segments of the conduit 11, increases.
Systems represented by the graph 409 in FIG. 20 can be said to be
conditionally stable, i.e, if they are operated at an operating
point 420 for which the flow in the forward direction is
sufficiently different from zero so that fluctuations in flow are
very unlikely to drive the flow into the reverse mode, then the
system will operate properly as a commpressor, driving working
fluid in the forward direction. Such compression systems can be
made unconditionally stable, i.e., stable independent of whether
they are forced in a reverse mode or not, by coupling them with
mechanical impedance means (e.g., fluid traps disclosed in my
above-identified pending patent application and herein below)
providing a relationship between flow and pressure as indicated
graphically in FIG. 21. In FIG. 21, curve 415 represents flow in
the forward direction through this impedance, curve 416 represents
flow in the reverse direction through the impedance, and the gap
G.sub.3 in the pressure in the region of zero flow represents the
change in pressure required to force this impedance into the
reverse flow mode. As long as gap G.sub.3 is larger than the gap,
G.sub.1 or G.sub.2 (FIG. 20), appearing when the compressor is
forced into reverse flow at small flow levels, the system will be
unconditionally stable in the vicinity of zero flow. Operation in
this mode is illustrated graphically in FIG. 21 by curve 413
(forward mode) and curve 414 (reverse mode). Gap G.sub.4 represents
Gap G.sub.3 algebraically summed with gap G.sub.2, and is the
amount of pressure required, beyond the back-pressure at which the
compressor has zero flow, to force flow backwards through the
compressor. Note that at no point does curve 414 enter the second
quadrant of the graph, which would represent pumping of working
fluid in the reverse direction.
Also, there is a gap G.sub.5 between the greatest forward
compression and the least reverse flow pressure. This ensures that
a set of parallel branches of a compressor can operate together
without some branches forcing working fluid back through
others.
PARALLEL-BRANCH INSTABILITIES AND STABILIZATION
Although the basic physical nature is the same, there is a useful
difference between the form of instability which occurs in a
gaseous rotary inertial thermodynamic cooler containing a set of
branches connected in parallal and that which can occur in a rotary
inertial thermodynamic compressor containing a set of parallel
branches. In the case of the cooler, the instability is believed to
consist of an excessively rapid flow of working fluid through one
of the branches of the system. In this type of instability, working
fluid flows through the branch in the desired direction. In the
case of the compressor, the form of the instability is believed to
be that flow through one branch of the compressor is reversed.
Therefore, there are a number of techniques which can be used in
the compressor to avoid this reversal of flow and thereby make the
system unconditionally stable which are not available for use in
stabilizing the cooler. This is made especially clear by FIG.
21.
One of the simplest devices which will produce the assymmetric
behavior with respect to flow, represented by FIG. 21, is a check
valve. For example, this could be a flap valve or ball valve which
opens to allow flow in the forward direction and closes to prevent
flow in the reverse direction. Alternatively, it could be a liquid
trap as disclosed and as is shown in FIG. 22 of the drawings
herein.
FIG. 22 shows an impedance control means 420 with an
outwardly-extending conduit section 421, an inwardly-extending
section 424, and a broad chamber 422 between sections 421 and 424.
The chamber 422 has an inlet port 427. The liquid 423 is held
against the outer wall 425 of the chamber 422 by centrifugal force
caused by rotation of the device about the axis 1. For a gaseous
working fluid to flow in the direction indicated by arrow 428, it
need have only enough pressure to bubble up through the shallow
liquid 423 in chamber 422 and then out through exit conduit section
424. For the gas to pass through the trap in the opposite (reverse)
direction, the gas must push liquid 423 back up into conduit
section 421 a substantially greater radial distance than it must
push the liquid in order to flow in the forward direction. This
introduces a pressure gap corresponding to G.sub.3 in FIG. 21, and,
in effect, forms a type of check valve. Branches identical to the
one shown in FIG. 22 can be connected in parallel if desired.
FIG. 23 shows a compressor 430 like that shown in FIG. 5, except
that it has plural parallel branches instead of one, a plenum 431,
and a flap valve 432 near the outlet of each branch. This
compression system is unconditionally stable against excessive
back-pressure at outlet 49. Additional branches, each with its own
check valve 432, can be added as desired.
It is possible to use several forms of stabilization simultaneously
in the same device. For instance, the heat exchangers might be
coupled to high-impedance heat sources so as to enhance the
protection against reversal of flow. Examples of high-impedance
heat sources which might be utilized in this way are, in addition
to a flame burning a fixed amount of fuel per unit time, the decay
of a radioisotope heat source, radiation heating, electromagnetic
inductive heating, etc. In another embodiment, the same
electromagnetic induction field which transfers thermal energy to
the heat exchangers might also provide a rotating electromagnetic
field which, by its electromagnetic drag on the rotating system,
rotates the device about the axis 1. For practical reasons,
generally it is preferable that this high impedance be achieved by
having a high thermodynamic impedance between the environment and
the heat exchange means, rather than by a high impedance between
the heat exchange means and the working fluid itself. This insures
that the heat exchange means within the compressor will not have a
temperature very much higher than that of the working fluid and
tends to protect the working fluid from thermal degradation.
Use of an unconditionally stabilized rotary inertial thermodynamic
compressor with multiple branches facilitates the construction of a
system in which the same compressor is capable of providing a small
amount of flow into a very high back pressure and/or a large amount
of flow into a low back pressure. For instance, one of the branches
in a multiple branch system can have a large number of rotary
inertial thermodynamic compression stages cascaded. This allows it
to produce a very high pressure at its delivery outlet. This would
be delivered through an appropriate check valve into the output
plenum. In the face of such back pressure, the other branches in
the system would have zero flow. Flow would not go backwards
through them because of their check valves. The other branches
would not cause an appreciable thermodynamic loss, because with
essentially negligible flow within them, the fluid in them would
absorb essentially negligible amounts of heat from their heat
exchangers. The thermodynamic and/or mechanical impedance of the
cascaded branch of the compression system can be chosen high enough
so that when there is a large flow at low pressure, the fraction of
the working fluid passing through the cascaded assembly is small
compared to the fraction of working fluid passing through the other
parallel branches. In that case, the amount of heat absorbed from
the heat exchangers in the high compression cascaded branch can
also be made small, so that heat absorbed by this branch causes
only a small thermodynamic loss.
GASEOUS-LIQUID THERMODYNAMIC DEVICES
For a number of applications it is possible to construct a rotary
inertial thermodynamic compressor in which the conduits extending
away from the axis of rotation and those returning towards the axis
of rotation operate at essentially the same temperature. During
operation, differences in temperature in the working fluid
necessary to provide differences in density, which, in turn, cause
compression, arise from the differences in the thermodynamic
impedances through which heat is coupled into and out of the
working fluid in the various conduit segments.
In FIG. 24 is shown a compressor 549 of the type described in the
preceding paragraph. Flow in the forward direction is represented
by the arrow 550. A system of this type is capable of pumping a
working fluid in either direction. For purposes of discussion, it
will be assumed that working fluid entering the system for either
direction of flow is at temperature substantially below that of a
heat source 557. Cool working fluid enters devce 549 at inlet 551,
proceeds radilly outward through conduit segment 552, radially
inwardly through conduit segment 533, which is in thermal contact
with conduit segment 552, and leaves the system through outlet 556.
Conduit segment 553 includes heat exchange means 554 and adiabatic
expansion region 555. In conduit segment 552 and adibatic expansion
region 555 there is a relatively high thermodynamic impedance for
transfer of thermal enery from the working fluid to the walls of
the system, or from the walls of the system to the working fluid.
When the working fluid is moving with very low flow velocity, this
heat transfer is adequate to insure that the working fluid be
essentially in thermal equilibrium with its environment. This
provides for a isothermal compression and expansion. In that case,
the compressor 549 gives very little compression. This is
represented graphically in FIG. 25 by curve portion 559. In the
region near zero flow, the compression available from this system
in either the forward or reverse direction, is very small. As the
rate of flow increases the forward direction, the effectiveness of
heat transfer in conduit segment 552 and adiabatic expansion region
555 is sufficiently small so that the compression of working fluid
in conduit segment 552 and its expansion in region 555 become
essentially adiabatic. Under such circumstances, the behavior of
the compressor 549 becomes essentially that of the compressor shown
in FIG. 5. Working fluid at a relatively low temperature enters
through inlet 551, experiences adiabatic compression on progressing
radially outwardly in conduit segment 552, expands relatively
isothermally in heat exchange means 554 within conduit segment 553,
absorbing heat from heat source 557, expands essentially
adiabatically in expansion region 555, and leaves the system at
outlet 556. In the absence of other mechanisms for stabilizing the
flow of working fluid within rotary inertial thermodynamic
compressor 558, it is necessary to operate on a portion of the
curve 559 in FIG. 25 for which the slope of the tangent line 561 is
positive. Recalling the sign convention of P as being the pressure
at the inlet minus the pressure at the outlet, quadrants 2 and 4 in
FIG. 25 represent compression, respectively, in the reverse and
forward flow directions. For forward flows greater than the value
represented by dotted line 560, a small increase in the amount of
flow results in a decrease in the driving compression produced by
the compressor. This, in turn, allows the amount of flow to return
to its initial value. Similarly, a decrease in flow below the
chosen operating line, but not less than line 560, results in an
increase in the driving pressure, restoring the flow to its
original rate. In this way the operation of the system is
stabilized. Similarly, flow in the reverse direction at magnitude
greater than represented by dotted line 562 leads to an impedance,
for small fluctuations, which also has positive slope. Operating
points further to the left of dotted line 562 and lying in the
second quadrant represent stable compression for reverse flow.
One advantageous feature of the compression 549 is that its
operation is dependent upon the differences in thermodynamic
impedance in conduit sections 552 and 553, which, for purposes of
discussion, can be regarded as arising from heat-exchange means 554
located within conduit segment 553 and the properties of heat
source 557 to which it is thermodynamically coupled.
GASEOUS-LIQUID THERMODYNAMIC DEVICES
All of the rotary inertial thermodynamic devices discussed thus far
utilize working fluids whose state does not change within the
device. For a number of applications it is desirable to use devices
within which the working fluid changes from a gas to a liquid or a
liquid to a gas; see, for example, my U.S. Pat. No. 3,470,704,
FIGS. 4 and 8, and my above-identified U.S. Pat. No. 3,808,828. In
general, operation of the systems to be discussed below will deemd
upon changes of a gaseous working fluid into liquid working fluid,
as by evaporation and condensation, and/or the absorption and
evolution of a gaseous working fluid by a liquid working fluid.
FIG. 26 shows one form of condensation and evaporation rotary
inertial thermodynamic cooling device. The forward direction of
flow is indicated by arrow 579. Pressurized gas is introduced into
the system through an inlet 580 and flows into a condensation
chamber 581. Condensation chamber 581 is equipped with heat
exchange means (not shown) having a thermodynamic impedance Z44 for
coupling heat from working fluid within chamber 581 to the external
environment. The gas condenses in chamber 581 and loses its heat of
condensation through the impedance Z44. The condensed liquid 586
accumulates against outer wall 583 of chamber 581 under the
influence of rotary inertial forces, and drains into a rotary
inertial trap 585 having a mechanical impedance Z45. The liquid
proceeds through the trap 585 into evaporation chamber 591 where it
evaporates at a reduced pressure, extracting from its environment
the heat of vaporization necessary for this evaporation through an
impedance Z46. This impedance Z46 includes the impedance of the
source from which heat is extracted and all intermediate heat
exchange means. Gaseous-form working fluid proceeds radially
inwardly through region 589 of evaporation chamber 591 and leaves
the system through an outlet 590.
For operation as a refrigerator, the gas at inlet 580 has a higher
pressure than at the outlet 590. The difference in gas pressure
between chambers 581 and 591 is counterbalanced by a difference R
in the radial location of surfaces 592 and 593 of the liquid 586.
This difference, acted upon by the rotary inertial forces, is
utilized to give rise to quite a substantial back-pressure, to
provide for the condensation at relatively high pressure of gas in
the chamber 581.
One advantgeous feature of the mechanical impedance Z 45 of the
trap 585 is that its value is adjusted automatically to provide
exactly the amount of back-pressure necessary to counterbalance the
gas pressures acting upon it, regardless of the variation of flow
rate over a wide range, and regardless of the variation of
impedances Z44 and Z46 over a wide range. It is this self-adjusting
feature that makes operation of the trap thermodynamically
reversible, i.e., at no point is a working fluid delivered through
a mechanical constraint at an appreciable difference in pressure.
The stabilizing effect of this self-adjusting form of mechanical
impedance can be seen readily by considering the case in which
impedance Z44, through which heat is rejected from condensing gas
in chamber 581, and impedance Z46, through which heat of
evaporization is supplied to the evaporating liquid in chamber 591,
both are made relatively large. As these impedances are made
larger, for a given flow, the pressure drop across the whole cooler
594 becomes larger. The result of this increased pressure drop is
that the difference R between radial locations of surfaces 592 and
593 becomes larger. However, the gas is not allowed to move freely
(bubble) from chamber 581 to chamber 591 until a very large gas
pressure (e.g., several hundred p.s.i.) is developed. Thus, the
trap operates effectively over a wide range of operational
parameters.
The use of traps such as the trap 585 in rotary inertial
thermodynamic systems is shown in FIGS. 1, 2, 3, 5, 6, 8, 9, 10 and
15 of my above-identified co-pending patent application. A rotary
inertial thermodynamic cooling system has been constructed and
successfully tested. It uses a refrigeration section of the type
shown in FIG. 26 and a cascaded gaseous rotary inertial
thermodynamic compressor of the general form shown in FIGS. 12 and
13.
The rotary inertial thermodynamic device 594 is thermodynamically
reversible, and therefore can be operated as a compressor. In this
modification of the operation of the FIG. 26 device, working fluid
enters the rotary inertial thermodynamic compressor device at inlet
580, as before. The fluid proceeds in the direction indicated by
arrows 579 into chamber 581. The working fluid entering the system
may be in the form of either a liquid or a gas. If it is in the
form of a liquid, then impedance Z44 is not important to the
operation of the device. Heat is added from a heat source (not
shown) to the liquid at surface 587 of chamber 591 to evaporate the
liquid in chamber 591. The inner surface 604 of the liquid, in the
case where the chamber 581 is not entirely filled with liquid, is
indicated in dashed outline. For operation as a compressor, this
inner surface 604 is radially inward from the surface 605 of the
liquid in chamber 591. The difference in the radial distances of
these two surfaces from axis 1 is designated R.sub.1. From chamber
581 liquid flows through the trap 585 and thence to chamber 591,
wherein it evaporates at a pressure greater than that in chamber
51. Vapor form working fluid proceeds radially inward within
chamber 591, and leaves the system at outlet port 590. The inlet
580 and outlet 590 do not have to be on the axis 1.
Careful examination of the operation of device 594 shows that
impedance Z45 is distributed throughout the system, in the sense
that it depends upon the levels 604 and 605 to which the liquid
working fluid approaches axis 1 in chambers 581 and 591.
Operation of the device 594 as a compressor is illustrated in FIG.
27. Using the previous convention that P represents pressure at
inlet minus pressure at outlet, two different conditions have been
shown. Curve 612 describes the case in which impedance Z46, the
impedance of the heat transfer into chamber 591, is relatively
large. Curve 613 describes the case in which Z46 is relatively
small. Curve 614, representing reverse flow, applies to both
cases.
In the case in which the impedance Z46 is relatively small, the
temperature of working fluid evaporating in chamber 591 is
essentially the temperature of the heat source, and the temperature
does not decrease appreciably as the amount of heat flowing
increases. The vapor pressure of the liquid working fluid depends
upon its temperature. Holding the temperature relatively constant
ensures that the vapor pressure will be relatively constant. This
gives rise to the relatively flat relationship between pressure and
flow, shown graphically by line segment 613. Therefore, if the
outlet of device 594 is blocked, the pressure in chamber 591 does
not increase to a high value; it increases only until the delivery
pressure reaches the vapor pressure of the liquid at the
temperature of the heat source, or, until evaporation of working
fluid within chamber 591 completely empties chamber 591, so that
liquid is no longer exposed to the heat source through the
impedance Z46. In FIG. 27 line segment 613 represents an operating
point at which the temperature of the heat source is not high
enough to cause a vapor pressure in the chamber 591 sufficient to
empty chamber 591.
In the case where Z46 is relatively large, as represented
graphically in FIG. 27 by line segment 612, as the flow rate
increases, the temperature of the working fluid during evaporation
in chamber 591 decreases. This is because the more rapidly the
working fluid flows, the more heat flow is required from the heat
source in order to evaporate working fluid in chamber 591.
Therefore, the temperature drop across Z46 is larger. As the
temperature of the evaporating working fluid drops with increasing
flow, so also does the vapor pressure available to provide
compression. It is for this reason that there is a relatively sharp
drop in compression with increasing flow of working fluid. As the
flow rate decreases, the temperature of the evaporating working
fluid increases. This increased temperature gives rise to an
increased vapor pressure with a corresponding increase of delivery
pressure available at the outlet. This process continues until the
pressure becomes so great that working fluid in liquid form is
completely cleared from chamber 591, back into trap 585. At that
point, liquid working fluid only enters chamber 591 as rapidly as
gaseous form working fluid is allowed to be delivered through
outlet 590. In the latter mode of operation, the pressure delivered
by the compressor 594 becomes essentially independent of the rate
of flow of working fluid therein. This is shown graphically in FIG.
27 by line segment 615. From line segments 613, and 612 with 615,
we see that the device is not capable of producing sufficient
forward compression to empty its trap 585 and thereby render itself
relatively susceptible to reverse flow.
Were we to connect a device of the type shown in FIG. 16 to a
mechanism which pushes gas through it in the reverse direction, it
would be necessary for that mechanism to produce a back-pressure
sufficient to overcome the pressure created by the difference in
radial surface positions between the outermost point of the inner
wall 582 of trap 585 and the innermost point to which working fluid
would reach in chamber 581, equal to the maximum forward
compression plus a pressure gap marked "G" in FIG. 27. With such a
back-pressure, the gas would bubble back through trap 585 and
chamber 581. This is illustrated by line segment 614 in FIG. 27,
which shows that, with reverse flow of this form, the reverse
pressure does not depend strongly on the amount of flow. This is
because the mechanical impedance due to friction is presumed to be
relatively small.
The pressure gap G can be relatively large. This serves effectively
to stabilize operation of the device. A device of this type is
unconditionally stable in the sense previously defined. From the
foregoing discussion of the stability of rotary inertial
thermodynamic compressors containing multiple branches operating in
parallel, it is clear that a flow-pressure relationship of the type
shown in FIG. 27 makes the device 594 especially suitable for use
in parallel configuration.
The device 594 offers a particularly clear example of a
relationship between internal flow of a working fluid within a
rotary inertial thermodynamic device, and external and internal
thermodynamic impedances through which heat is transferred to or
from the working fluid. The differences between line segment 613,
and line segment 612 and 615 taken together, arise without need for
changes in the internal structure of the device, but rather just by
changing the thermodynamic impedances with which its is coupled to
a heat source. Clearly, a rotary inertial thermodynamic system
including a device of this form should be anaylzed by treating the
device as part of a larger system including its internal impedances
and also the external impedances of the environment with which it
interacts. This is true, whether the device is a part of a
sealed-conduit device, all of which rotates as a single unit, or is
part of a hybrid system----hybrid in the sense that part of it
rotates and part of it is stationary, with couplings through
rotating seals between the rotating part and the stationary part
whenever needed, or in the sense that parts rotating with different
velocities are co-gained for fluid flow.
From the previous discussions of stability of rotary inertial
thermodynamic compressors containing multiple branches connected in
parallel, it can be seen that the use of a device as shown in FIG.
26 in each branch, possibly in combination with other compression
means in the branch, can serve to stabilize the composite
compressor. If desired, it is possible to utilize various impedance
means in combination to render each of the branches unconditionally
stable; device 594 is effective as such as a means. It also is
possible to utilize various different types of compression devices
in the various branches, i.e., it is not necessary for all of them
to utilize the same internal geometry or construction
techniques.
The angular velocity with which the device shown in FIG. 26 is
rotated affects the maximum back pressure into which the device can
deliver working fluid. For rotary inertial thermodynamic devices of
the type shown in FIG. 26, the angular velocity at which the device
is rotated usually strongly affects the thermodynamic and
mechanical impedances.
Forepump For Stabilization
Rotary inertial thermodynamic compressors of the type shown in FIG.
26 require a certain minimum input gas pressure for proper
operation, because liquid must be present within the trap 585. If
the available gas source cannot meet the requirements, a device 723
of the type shown in FIG. 28 may be utilized. This is one example
of a general class of systems utilizing part of the compressed
gaseous working fluid delivered by the rotary inertial
thermodynamic compressor to actuate a forepump or other secondary
pump, in this case, raising the pressure of the gas available at
the intake to a high enough value to allow proper or efficient
operation of a compressor.
The device 723 has an inlet 707 which receives gas flowing in the
direction designated by arrow 706. 708 generally designates a
forepump, in this case containing an expansion nozzle 709 and a
diffuser 710, which together serve as a jet pump to drive gaseous
working fluid into a condensation chamber 711 at a higher pressure
than is available at inlet 707. Chamber 711 contains intermediate
pressure gas 713, which condenses, delivering its heat of
condensation to an external environment through thermodynamic
impedance Z719. The condensed liquid 716 collects at the outermost
portion of chamber 711 and drains into a rotary inertial trap 715,
and flows in the direction of arrow 725 into an evaporation chamber
718. The differences in liquid levels 712 and 717 in conduit
segment 715 and chamber 718, respectively, acted upon by
centrifugal forces, provides the necessary driving pressure
utilized in producing high-pressure gas for delivery at the outlet
726 of the device 723. The heat of vaporization required to
evaporate the liquid in chamber 718 is supplied by a heat source
724 through a thermodynamic impedance Z720. The high-pressure
vapor, designated 714, flows radially inwardly through conduit
segment 727 and divides into two streams, one leaving at the outlet
in the direction designated by arrow 712, and the other returning
through a high-pressure conduit 722 to actuate the forepump 708.
Further details of such a forepump are given in my above-identified
co-pending application.
The forepump, shown in the form of a jet pump, supplies sufficient
working fluid so that the system never turns off at its intake or
outlet. Even if the amount of working fluid entering the system is
essentially zero, if it is operating into a back pressure at outlet
726, and if there is a pressure difference sufficient to maintain
adequate flow in jet nozzle 709, the input to the liquid and gas
rotary inertial thermodynamic compressor will be sufficient to
produce the necessary condensation in chamber 711 and keep that
portion of the system operating. For this reason, a device of this
type is not susceptible to flow reversal merely be reduction of
intake pressure. The forepump means renders the device stable over
a wider range of flow input impedance. At the same time, it raises
the working fluid pressure in condensor chamber 711, allowing
condensation to occur at a higher temperature. This allows the heat
of condensation to be rejected through a higher thermodynamic
impedance, without interferring with stable operation of the
device, than might otherwise be the case.
All of the rotary inertial thermodynamic gaseous compressors
previously discussed operated on a ratio; that is, the input
pressure was assumed fixed, and the difference in pressure between
output and input was then evaluated.
In place of the rotary inertial compressor in FIG. 28 of the type
appearing in FIG. 26, one can use a gaseous compressor such as in
FIGS. 5 or 10. Forepump means 708 then serves to increase the input
pressure to the inlet of the gaseous compressor which, by the
nature of its operation, muliplies its input pressure. Use of the
forepump means reduces the input impedance of the composite device.
Also, flow through the forepump jet can prevent flow through the
compressor from entering the unstable region near zero flow. In
both these ways, the forepump can serve to stabilize operation of a
rotary inertial thermodynamic compressor. It also serves to reduce
the number of stages required for a given compressor ratio and/or
to increase the maximum compression ratio available from the
composite system. A composite device of this type can be made which
will not be forced into reverse flow by an arbitarily large source
or load impedance.
As was discussed in greater detail earlier, the operation of the
systems described herein, utilizing a flow of gas in a rotor and
depending upon temperature-dependent differences in density in that
gas for their thermodynamic effects, depends upon the ratio of
inlet and outlet pressures. For simplicity in discussing these
effects, the ratio is discussed in terms of the pressure difference
across the device, assuming that either the inlet or the outlet
pressure is held constant. The physical reasons for the dependence
upon ratio of pressures rather than pressure differences, and the
way in which this can be taken into account, was discussed in
detail. This should be borne in mind with respect to the graphs
herein showing pressure difference versus flow in gaseous working
fluid devices. In addition, in general, the effects of changing the
angular velocity of rotation have not been discussed in explaining
the stability and instability of flows within the rotary inertial
thermodynamic devices. The reason for this is that the stability or
instability of the flows has essentially the same dependence on
pressures and thermodynamic impedances at various angular
velocities, except for scale factors which are dependent upon the
angular velocity. The essential features required to understand the
principles for stabilizing these systems can be set forth and
understood by considering systems rotating with constant angular
velocity. Ways in which variations in angular velocity can be
utilized to alter impedances have as their physical basis the
dependence of centifugal and coriolis forces on angular
velocity.
Basic to the operation of rotary inertial thermodynamic compressors
is the availability of thermal energy within the rotating system.
Associated with the ways in which this thermal energy can be made
available are characteristic thermodynamic impedances which, in
turn, influence the behavior of the system, of which this rotary
inertial thermodynamic device is a component. The mechanisms by
which thermal energy are made available within the rotating device
can be combined with the mechanisms which serve to provide the
necessary rotation. In the calculation of Carnot efficiency for a
compressor viewed as a heat engine, the overall performance is more
sensitive to fluctuations in the heat rejection temperature than in
the heat absorption temperature. This is because the same change in
temperature represents a larger fraction of the overall
temperature, because the temperature at which the heat is rejected
is smaller than the temperature at which the heat is absorbed.
Therefore, it is desirable to keep the impedance for the rejection
of heat as small as feasible. For most of the operating points
which would occur in systems of this type, the temperature for heat
rejection is sufficiently low so that radiant heat transport is not
an adequate means for removing the heat present. Also, typically,
thermal conduction is not an efficient means for transporting heat
out of a rotating device. For these reasons, the mechanism of heat
transport used for removing heat from the rotating device is
typically convective, that is, the heat is transported by the
transport of some fluid. In a single-stage rotary inertial
thermodynamic gaseous compressor, this transport of heat occurs by
the transfer of working fluid from the device performing the
compression. If this transfer is to a stationary component in a
hydrid system, the transfer of heat from the rotating device has
occurred by the transfer of this working fluid. In the event that
the compressor is part of a larger rotary inertial thermodynamic
device, all of which rotates together, the heat rejection occurs by
heat exchange through some surfaces to some moving medium. In the
location in which the heat rejection is required, a gaseous
compressor is different from a gaseous cooling system. In a gaseous
compressor, the heat exchange for rejection occurs relatively near
the axis, allowing a larger coolant flow with relatively small
momentum transfer. In comparison, a cooling device requires heat
transfer at points relatively far from the axis of rotation, having
associated therewith higher tangential velocities and larger
momentum transfer per unit of heat transfer to a coolant. In the
following sections, I will discuss ways in which heat can be
transferred into and out of a rotary inertial thermodynamic device
and discuss the characteristics of the thermodynamic impedances
associated with the various means of heat transfer. This is not a
complete enumeration of means of transfer, but rather a
representative list serving to characterize the impedances and the
dependence of the impedance on the physical form of heat
transfer.
Heat Sources
It is to be understood that, where required by the processes
occurring therein, rotary inertial devices are provided with
heating and heat rejection means. These means can be used in many
combinations. For simplicity, heating and heat rejection means are
disposed separately. In the figures, one or more means may appear
in the same diagram, and, for simplicity, occasionally heating or
heat rejection means may be omitted from a diagram intended to
illustrate another means, without any application about the
necessity of omitted means.
Radiant Heat Sources
In FIG. 29, 1 is the axis of rotation, 761 generally designates the
radiant energy source, e.g., a lamp 750 with reflector 760. 764 is
the rotary inertial thermodynamic device to be heated, and 762 is
the surface of device 764 upon which radiant energy impinges to
produce heating. 763 is an optically transparent, or nearly
transparent, body of insulating material which allows radiant
transfer of heat to surface 762 while reducing heat loss by
convection and conduction to the surrounding medium. The radiant
energy source 761 can either be an artificial source of radiant
energy or a natural source, such as the sun. With suitable use of
an optical system, not shown, solar energy can be caused to impinge
upon and heat the surface 762. This heat transfer technique can
also work in a vacuum. Portions of the device can be heated
differently by presenting a surface with different absorbtivity to
the radiant flux.
Internal Heat Sources
Another form of heating is provided by a heat source which
generates the heat within the rotating device itself without
external coupling to the environment. Among such sources are
radioisotope sources which release thermal energy by their decay;
nuclear fission fuel elements, which can be utilized in part of a
reactor to provide heat to the medium surrounding them without
appreciable transfer of momentum; fully contained chemical
reactions proceeding within the rotating device; and, potentially,
fusion to release energy from nuclei. With these forms of heat
production within the rotating device itself, heat can be delivered
wherever it is needed for maximum thermodynamic efficiency. In
particular, heat exchangers buried deep within a thermally
insulating structure can be heated in this way so as to insure that
essentially all of the heat introduced is utilized in the
thermodynamic processes in the rotating device.
Inductive Heat Sources
Electrically conductive components of a rotary inertial
thermodynamic device with suitable electrical resistance can be
heated by electromagnetic induction. As in the case of heat
generation from energy sources within the rotary device, this also
allows selective heating of components of the device buried deep
within insulating members.
The necessary time dependent magnetic field required for
electromagnetic induction can be produced in several ways. One way
is to rotate the components of the rotary system through a
stationary magnetic field with spatial dependence of the field. The
drag induced by the passage of the components through the magnetic
field is then a mechanism by which mechanical shaft work is
converted to heating of the buried components. Alternatively, the
electromagnetic field can be generated by varying a magnetic field
with a characteristic direction of rotation, as is conventionally
done in a polyphase motor. This rotating magnetic field can serve
two purposes. It can heat the heat transfer means within the rotary
inertial thermodynamic device, while the drag between the
components so heated and the rotating magnetic field rotates the
device.
The foregoing arrangement is illustrated in FIG. 30, in which 765
is the rotary inertial thermoynamic device, in which are buried
heat exchange means 766 which have the appropriate electrical
conductive impedance and heat transfer properties. For example,
exchangers 766 might be simple strips of conducting material, or
sintered porous metal plugs with many fine passageways. 767 is an
electromagnet assembly having a suitable core 771, and a winding
772 connected to a suitable alternating current power source 773. A
multiplicity of such magnetic elements can be utilized. 768 denotes
generally a permanent magnet 769 and pole pieces 770. A shaft 771
is mounted on bearings (not shown) and is usedto support the device
765 for rotation about an axis of rotation 1. In this arrangement,
the rotor serves as the rotor of an alternating current motor.
Additional heating can be produced within this rotor by the
utilization of the stationary magnetic drag field produced by one
or more optional stationary magnet assemblies 768. The amount of
torque produced by the electromagnet assembly or assemblies 767,
and the amount of heating produced thereby, can be separately
controlled by controlling the frequency of the power source 773, or
by the use of drag fields, or by controlling the phase of power to
several electromagnetic assemblies 767. These electromagnetic
heating techniques offer a way of simplifying the drive means for
rotary inertial thermodynamic devices. These means for heating and
rotating operate in many kinds of environments, including a
vacuum.
Dielectric Heat Sources
Dielectric heating also can be used to create heating within the
housing device. High-frequency magnetic hysteresis heating also can
be used. A dielectric heating arrangement is shown schematically in
dotted lines in FIG. 30. Plates 775 are positioned on opposite
sides of the rotary device 765. The plates are connected to a
source 776 which supplies an appropriate high-frequency alternating
voltage across the plates. The plates are positioned so as to
provide a rapidly alternating electric flied which heats a
dielectric material in the device 765. The plates are positioned,
of course, so that only the desired portions of the rotary device
765 are heated. Portions to be heated are preferably made of a
material with a large loss tangent at te field frequency, while
other parts are made of a relatively low-loss dielectric material.
For example, ferroelectric ceramics, such as barium titanates are
available, which can be made to have an adequately large
loss-tangent. "Mylar", polystyrene, and many other plastics, and
many other ceramics have low loss tangents. Some low loss-tangent
materials, for example, beryllium oxide also possess high thermal
conductivity, and are suitable for conductive heat transfer. Both
dielectric and induction heating are shown in the same figure for
simplicity. Typically, they would be used separately. Means for
heat rejection (not shown) such as, for example, those shown in
FIGS. 34 and 35, can be utilized if required by the thermodynamic
process occurring within the rotor. Some devices, such as
single-stage gaseous compressors, can reject heat with stroking
fluid leaving the device, without special provision for separate
rejection of heat.
Internal Fuel Burning
Another method for heating is to burn fuel within the rotating
device. FIG. 31 shows an arrangement for this purpose. 777
designates generally a rotary inertial thermodynamic device to be
heated. An intake for air is at 778, and a fuel inlet is at 799.
The fuel-air mixture passes outwardly through conduit means 783
past combustion stabilizing means 780 (e.g., screens) into
combustion region 782, and thence out of the rotating device
through nozzles 781. Alternatively, the combustion products can be
returned nearer to the axis of rotation and discharged from the
rotating device through appropriate conduit means, not shown.
Suitable ignition means, not shown, can consist of a small spark
plug or glow plug, with, for example, piezoelectric actuators for a
spark plug. The jet nozzles 781 are oriented so that their exhausts
are in the same direction, and contribute reaction torque to
produce or augment rotation in the device 777, as is explained more
fully in my above-identified co-pending application.
Electron Beam Heating
Yet another technique for transferring heat into a rotary inertial
thermodynamic device is bombardment with an electron beam. In FIG.
32 is illustrated a vacuum device utilizing electron bombardment
for heating a rotary inertial thermodynamic device 805 secured to a
shaft 802. 804 is a stationary vacuum chamber surrounding the
device 805, and 803 are suitable rotary seals. The shaft 802 and
the device 805 rotate about the axis of rotation 1, and the seals
803 maintain the vacuum in the chamber 804. A suitable electron gun
806 is utilized for the bombardment of the device 805 in order to
produce heating at selected locations therein. Electron gun 805
operates from power supply 807. The details of the electron
bombardment device are not shown explicitly. Many devices are
known, especially in the art of thin film evaporation and
deposition in vacuum, where they are utilized extensively for
heating evaporation sources. Many types of seals are known which
can be utilized for seal 803. Especially useful seals are those
during ferro-magnetic fluid suspensions. The evacuation means for
vacuum chamber 804 is not shown.
Vapor (Steam) Heating
Steam, or other actuating vapor, often is available as a source of
thermal energy. It is feasible to both heat and spin a rotary
inertial thermodynamic device utilizing a vapor as an actuating
field. For specificity, consider water vapor (steam). In FIG. 45 is
shown another embodiment in which the rotary inertial thermodynamic
device 811 is shown with vanes 814, and a shroud 812. Vapor is
directed obliquely against the vanes 814 through a nozzle 813. The
vanes 814 serve both to augment the reaction of the vapor against
the rotating member and to transfer heat therefrom into the
rotating device 811. Condensate is collected in the shroud 812 and
leaves through a drain 815. By controlling the angle with which the
vapor jet causes vapor to impinge on blades 814, it is possible to
control independently the amount of rotational torque produced and
the amount of heating produced. The device heated can be part of a
larger rotating assembly containing other rotary thermodynamic
devices laying outside of the shroud 804.
Radiant heat transfer, electromagnetic induction and hysteresis,
dielectric heating, and electron bombardment readily can be used
for selective heating of portions of a rotary inertial
thermodynamic device, so that the heat can be applied to selected
regions in order to independently control processes occurring
within the device. Such regions can be located across an entire
surface of the device, including both radial and angular variations
in position. Variations in heating of locations about the axis of
rotation can be accomplished by modulation of the intensity of the
heat source. For example, the electron beam intensity can be
modulated. A light source can be modulated in intensity, or
operated as a succession of bright flashes using the same technique
as is used with stroboscopic lamps. Electromagnetic induction and
hysteresis, and dielectric heating can be modulated both as to
frequency and amplitude. In this way, it is possible to control
separately the temperatures of various parts.
Thermodynamic Valves
It also is possible to use gaseous compressors as valves, by
adjusting the pressure differences which can appear across them, or
to fill and empty traps so as to control flow. Localized heating
can be used to control the impedances of such traps.
In FIG. 33 is illustrated schematically a simple valve mechanism,
utilizing a chamber 817 containing a liquid 818. The chamber has an
outlet to a bellows 820. The chamber 817 is in thermal contact with
the surface 819 to which heat can be transferred selectively.
Localized heat energy is supplied to surface 819 from outside in a
suitably modulated fashion. The bellows receives vapor from the
chamber 820 and operates a valve 821. All of the elements 817, 818,
820 and 821 are inside of and rotate with the device 816, which can
be of any of a wide variety of forms. Device 816 rotates about axis
of rotation 1. For example, a multibranch and/or multistage
compressor can have branches and/or cascaded stages selectively
valved in this way to allow efficient operation at reduced
capacity, e.g., in a large industrial power plant.
In general, many of the forms of rotary inertial thermodynamic
devices which can produce or sustain a pressure difference across
their intakes and outlets can be utilized in conjunction with such
selective application of heat to provide means of controlling flow
or flows within a rotary inertial thermodynamic system.
In many cases it is possible to have a working fluid transport the
heat to be rejected by a rotary inertial thermodynamic compressor
from the rotating device. In those cases, no special provision need
be made for rejecting heat. However, in cascaded gaseous
compressors, in absorption cycle devices with closed cycles for the
absorbent fluid, and in many other forms of rotary inertial
thermodynamic device, it is necessary to reject heat from a
rotating member into its environment. Often, it is desirable that
the amount of mechanical eneryy lost from the system in performing
such heat transfer be minimized. In some cases it is possible to
use that energy which is consumed from the mechanical rotation of
the shaft to do some form of useful work in an external system. For
instance, the coolant can be circulated by means of an impeller
system rotating with the rotary inertial thermodynamic device.
Quite generally, there are many system configurations in which the
rotating member of the system can be caused to rotate by its
environment, and/or can be used to move parts of its environment.
For instance, as has been described above, a rotary inertial
thermodynamic device might be spun by steam and heated by it at the
same time. In turn, the device might be cooled by a flow of fluid,
e.g. water, which the device creates by its rotary motion.
Internal Liquid Cooling
The most efficient location for conveyance of heat from a rotating
device by means of heat exchange with an external fluid is at the
hub. At the hub, the tangential velocities of the rotating members
are the smallest. Within the rotating device, heat can readily be
transported from a region internal to the device, from which it is
being rejected by a thermodynamic process occurring therein, to the
hub. In many cases, an efficient way to do this is to utilize
evaporative transfer. In FIG. 34 is shown schematically a device
utilizing such transfer to cool an internal surface 837 which is in
a region in which a thermodynamic process occurring within a rotary
device is required to reject heat.
In FIG. 34, 1 is the axis of rotation, 830 designates a rotary
inertial thermodynamic device within which is shown schematically a
heat transport mechanism comprising surface 837, volatile liquid
836, conduit means 838, chambers 841 and 839, and heat rejection
surface 835. Operation of this heat transport means is by
absorption of heat at 837, rejected by some process (through an
impedance) into the fluid 836, as indicated by the arrow 843. The
fluid 836, absorbing this heat, is caused to volatilize. The vapor
thus formed proceeds into and through conduit segment 838. Upon
reaching chamber 839 it contacts surface 835, condensing thereon,
to deliver its heat of vaporization to the surface 835. Liquid
formed by this condensation flows back through conduit 838 to
return to the pool of liquid 836 to complete the cycle and be ready
to absorb heat again from surface 837.
Although it is not necessary to combine the foregoing and the
following steps in the same device, at the hub 846 in FIG. 34 is
shown a means for rejecting the heat at surface 835 into a coolant
liquid circulating within the hub. This coolant enters at inlet 831
and leaves at outlet 832 in the direction shown by arrows 840.
Liquid flows to near the end of the hollow interior of the hub
through tube 834, flows outwardly, and returns through a rotary
seal 833 to outlet manifold 845 and outlet 832. In doing so the
liquid passes along the inner surface of hub 846, which is thereby
efficiently cooled and is available as a surface to which more heat
may be rejected.
The direction designated by arrows 840 in FIG. 34 is appropriate
for liquid flow. In the event that the coolant is operative in a
vapor to liquid vapor conversion, whereby it absorbs heat by
vaporization, the proper direction for most efficient operation is
counter to that designated by arrows 840. In the latter case, there
is evaporative cooling within chamber 846. A liquid film standing
against the outer wall, of which 835 is a segment, is used to
absorb heat, and its vapor is transported from the system to leave
at port 831.
OPERATION IN A VACUUM
For some applications, it may be desirable to operate a very high
speed rotary inertial thermodynamic device in vacuum. Within such
an environment one can use radiative heat transport. In FIG. 35 is
shown an illustration of such a system. The axis of rotation is 1.
861 is a shaft. 860 are seals. 864 is some mechanism for radiant
heating of rotary inertial thermodynamic device 863 rotating within
vacuum chamber 862. (in space, no vacuum chamber is required)
Evacuation means for vacuum chamber 862 is not shown. Rotary
inertial thermodynamic device 863 includes internal heat transport
means 872 and 873. 873 is utilized to transport heat from a region
where it is absorbed from radiant source 864. 872 is used to
transport heat to a heat rejection mechanism 866 from somewhere
internal to the rotary inertial device 863 where such heat is
rejected from some thermodynamic process. On heat rejection device
866 are located a plurality of thin fins 867, interleaved with
stationary fins 868 affixed to a heat rejection means 865. Fins 867
are in thermal contact with, and rotate with, the heat rejection
device 866. The rate at which energy is radiated from a black
surface at 300.degree. kelvin is approximately 0.046 watts / square
cm. or approximately 0.01 calories / square cm. second. By
interleaving very thin, closely spaced vanes it is possible to
achieve a sufficiently large area of radiating surface in the vanes
867 from which radiant energy can be transferred to the cooler
vanes 868. The rate at which energy is radiated from a black
surface is proportional to the fourth power of temperature of the
surface. By utilizing cooling mechanism 865 to cool the fins 868
interleaved with rotating fins 867, the amount of energy radiated
by fins 868 is substantially reduced so that an appreciable
radiative transport of heat from rotating vanes 867 to stationary
vanes 868 can be achieved.
Cooling means 865 in FIG. 35 includes a conduit 869 for conducting
a coolant fluid (e.g., water) into a cavity 879, and manifold means
870 for collecting fluid returning from the cavity, the direction
of flow being represented by arrows 871.
For some special-purpose applications the advantages of rotation at
very high speeds in a vacuum are greater than the disadvantages of
the structure required for radiative rejection of heat. The rate at
which heat is transported increases so rapidly with increasing
temperature that, for many applications in which a higher rejection
temperature can be tolerated, such a transport mechanism becomes an
acceptable means for rejecting heat from the rotating device 863.
Such means for rejecting heat are characterized by a thermodynamic
impedance, as are other means based on motion or evaporation of a
coolant.
HEAT PIPES FOR HEAT TRANSFER
Still referring to FIG. 35, embedded in the rotary inertial
thermodynamic device 863 is a heat pipe heat transport means 882,
consisting of a chamber 880 with a capillary material 881 within
it, and an appropriate amount of a suitable volatile working fluid.
The heat pipe 882 is operative to transport heat by evaporation of
some working fluid in contact with surface 883, which is heated by
radiant heat transfer means 864, and to transport vapor therefrom
to condense and deliver heat through impedance Z884 to some
thermodynamic process, with the condensate being returned to the
surface 883 by capillary action in the material 881.
In utilizing heat pipes for such heat transport within a rotary
inertial thermodynamic device, the augmented acceleration field
associated with the rotation of such a device, and its effect upon
the motion of the liquid working fluid utilized within the heat
pipe, should be taken into account. The magnitude of the
acceleration fields found in rapidly rotating devices of this type
makes it quite difficult for a capillary system to transport a
liquid form of working fluid radially inwardly by any great
distance. However, in devices rotating with relatively low angular
velocities, such capillary and vapor type transport systems
generally known as heat pipes are suitable for transporting heat
from one portion of the rotary device to another.
INTERNAL ELECTRICAL HEATING
An additional way for conveying thermal energy into a rotary
inertial thermodynamic device is to use a slipring assembly to
transfer electrical energy which is then utilized in some
appropriate form for producing heat within the device. In FIG. 36
is shown such a heating system. 1 is the axis of rotation, and 908
is a shaft carrying a rotary inertial thermodynamic device 909. A
pair of sliprings 911 on shaft 908 make electrical contact with a
pair of brushes 912, which are connected to a suitable power supply
913. Inside of the rotary device 909 is a suitable electrical
energy-to-heat conversion means, such as a resistance heating
element 910. This conversion means is connected electrically to the
sliprings 911. The thermodynamic impedance of this heat transfer
mechanism depends upon the detailed mechanism by which electrical
energy is converted to thermal energy, (e.g., positive and negative
coefficient thermistor heating elements, metals, etc.) and the
properties of the power supply used to deliver electrical energy to
the system. The effective thermodynamic impedance of such a heat
transfer mechanism can be adjusted over a very wide range. The
means utilized for conversion of electrical energy to thermal
energy can also participate in the operation of the rotary inertial
thermodynamic device in other ways. For instance, it can be
incorporated as part of a mechanical flow impedance and thus can
have intimate contact with the working fluid.
IMPEDANCES OF FOREGOING HEAT SOURCES AND DRAINS
Heating by means of radiant energy transfer, isotopes, magnetic
induction, combustion in a rotating system, electron bombardment
and combination of these means are characterized typically by a
high thermodynamic impedance; that is, the amount of energy
delivered to the rotating device being heated varies only slightly
with the temperature of the portion of the rotating device
receiving the heat. In the case of steam or other vapor heating,
the effective thermodynamic impedance of the source is much
smaller. In this case, the temperature of the portion of the
rotating device receiving heat is very nearly that of the
condensation of the vapor at the pressure involved. A decrease in
the temperature of the region at which condensation is occurring
results in a substantial increase in the amount of condensation
there. For this reason, the thermodynamic impedance of such a vapor
heat transfer process depends upon the mechanical impedance by
which the vapor is supplied to, and by which spent vapor and
condensate are removed from, the surfaces receiving heat.
Cooling of a rotating device by convection and evaporation are also
characterized by thermodynamic impedances, typically substantially
lower than those associated with the high-impedance heating
techniques mentioned above. Of these, typically evaporation
techniques have characteristically the lowest impedance, again
because of the dependence of the evaporation temperature upon
ambient pressure. In the case of evaporative cooling, as in
heating, the detailed thermodynamic impedances associated therewith
depend upon the mechanical impedances by which liquid is fed to and
vapor removed from the region where evaporation occurs.
Heat rejection through a radiative heat transport mechanism of the
type discussed in connection with FIG. 35 has a characteristic
thermodynamic impedance intermediate between those impedances
associated with mechanical fluid flows and vapor condensation and
evaporation, and those associated with radiant heating and isotope
heating. Isotope heating provides the highest impedance of all of
the types discussed above.
IMPEDANCE CONTROL FOR HEAT SOURCES AND DRAINS
It is possible to use a temperature-sensing process with feedback
to control the effective thermodynamic impedance by varying the
properties of the heat source in order to render either the rate of
flow of heat or the temperature of the receiving surface nearly
constant. If the rate of flow of heat is held essentially constant,
then the heat source has been stabilized in a very high
thermodynamic impedance mode. If the temperature of the receiving
surface or of any point selected within the thermodynamic system is
held constant, then the total thermodynamic impedance from the heat
source to that point becomes effectively very small.
In a similar fashion, feedback can be used to change the effective
impedance of the heat rejection means. For instance, the amount of
flow of coolant past a heat rejection surface can be controlled so
as to maintain the temperature of that surface essentially
constant, or so as to maintain the rate at which heat is removed by
the coolant essentially constant. These two cases correspond,
respectively, to an extremely low effective thermodynamic impedance
and an extremely high effective impedance. Of course, feedback can
be used to obtain impedances intermediate in value between these
extremes.
The transfer of heat into or out of a rotating device can be made
to depend upon some property of the materials used. For example, in
the case where heat transfer elements deep within an insulating
rotary inertial thermodynamic device are heated by electromagnetic
induction, the temperature of such elements can be maintained
essentially constant by utilizing the property of ferromagnetic
materials that above their curie temperatures they cease to be
ferromagnetic. In this way, the amount of electromagnetic induction
power drawn from an oscillating electromagnetic field can be
regulated by the element which is drawing that power itself. As its
temperature passes above the curie temperature, the amount of power
which it draws from the oscillating electromagnetic field decreases
substantially. Similarly, when its temperature drops below the
curie temperature, the amount of power drawn from the field
increases substantially. In this way, it serves as its own
temperature regulator. A corresponding effect is seen in some
dielectric materials, (e.g., ferroelectric ceramics) and might be
utilized to regulate their temperature in an oscillating electric
field.
Another way in which internal regulation can be achieved is by
means of a device of the type discussed in connection with FIG. 34,
in which a vapor transport system is utilized to transfer heat. The
properties of such a transport system depend strongly upon the
temperature. As the temperature of surface 837 in FIG. 34
increases, the vapor pressure available to drive vapor form working
fluid through conduit 838 increases, and, therefore, the capacity
of this mechanism to transport heat to surface 835, at which it is
rejected, increases. By choosing the liquid 836 appropriately, it
is possible to make this dependence of vapor pressure upon
temperature of surface 837 effective to limit the temperature of a
process rejecting heat into surface 837.
INTERNAL CHEMICAL REACTION: COMBUSTION
Thermal energy also can be introduced into a working fluid within a
rotary inertial thermodynamic device by having the energy appear
directly within the working fluid itself, rather than by using some
external means to couple heat energy into the fluid. For example, a
radiation absorbtive, or partially absorbtive, fluid can be exposed
to radiation (electromagnetic, particulate, etc.) which it absorbs,
thereby transferring the radiation energy directly into the fluid.
Or, the working fluid can be of such a nature as can support an
internal energy-releasing reaction, for instance, a mixture of fuel
and oxidizer.
FIG. 41 shows a rotary inertial thermodynamic gaseous compressor
utilizing such a working fluid which can support combustion.
Working fluid is introduced in the direction designated by arrow
1010 at an inlet 1011. It proceeds radially outwardly through
conduit segment 1012, within which is experiences essentially
adiabatic compression. Reaction stabilizing means 1013, e.g., a
screen, or catalyst, stabilizes a heat-producing chemical reaction
occurring in reaction zone 1014, within conduit segment 1016. After
this reaction zone the working fluid proceeds radially inward
through adiabatic expansion region 1015, to leave the device at
outlet 1017. Optionally, a portion of the high-pressure working
fluid can be bled from the system to operate some tangential jet,
designated 1018, or all of the working fluid can be returned to the
axis of rotation within conduit segment 1016. It is to be
understood that inlet 1011 and outlet 1017 do not have to be on the
axis of rotation, and that this rotary inertial thermodynamic
device can be part of a system including other portions which
rotate or are stationary.
INTERNAL NUCLEAR REACTION
FIG. 42 shows a system utilizing a nuclear reaction to produce heat
within a gaseous working fluid. Flow of working fluid is in the
direction designated by arrow 1019, entering at inlet 1024,
progressing radially outwardly through section 1020, within which
the working fluid experiences essentially adiabatic compression,
proceeding to a reaction chamber 1021, within which the nuclear
reaction occurs, progressing radially inwardly through adiabatic
expansion region 1022, and leaving through outlet 1023. Again, it
is to be understood that inlet 1024 and outlet 1023 do not have to
be located on the axis, and that this device can be used in simple
or hybrid rotary inertial thermodynamic systems.
An example of a suitable nuclear reaction in reactor 1021 would be
one using uranium hexafluoride as a working fluid. In the reactor
1021 is a known moderating structure 1025 for facilitating the
reaction. The reaction would occur within the reactor and not occur
elsewhere within the system. With certain types of nuclear fuel, a
moderator is not needed because the geometric configuration of the
reactor 1021 will ensure a satisfactory sustained reaction. The
geometry of the chamber can be utilized to localize the
reaction.
By utilizing the dependence of density of working fluid near the
periphery of the rotating device upon the speed of rotation, and
the fact that the reaction depends on the density of the fluid, a
system of this type could be made in which a reaction occurs only
when the device is rotating above a selected angular velocity. This
feature, together with the extreme simplicity of rotary inertial
thermodynamic systems, can give rise to a highly reliable device.
The angular velocity effect on density and distribution of working
fluid can be used to control the internal reaction rate in a sealed
system. In the case of a device which is not sealed, control can
also readily be effected by varying the gas pressure within the
device. Of course, the structure which is used to promote the
reaction within the working fluid does not all have to lie within
the rotating system itself; external nuclear reactor components,
including moderators, fuel, control rods, shields, etc. can be
used.
Rotary inertial thermodynamic compression devices which utilize a
chemical, nuclear or other reaction in the working fluid for
heating are specially suitable for the very high energy transfer
rates desirable in an engine application. Materials are available
for building compressors of this general form with thermodynamic
Carnot efficiencies in excess of 50%.
RADIATION-ABSORPTIVE WORKING FLUID
In any of the embodiments, a radiation absorbtive working fluid can
be used. The radiation field impinges upon the device in the region
of working fluid to be heated. For example, in FIG. 5, a radiation
field would impinge on conduit segment 62 in the region shown
occupied be heat exchange means 46, without means 46 present.
Similarly, regions occupied in FIG. 10 by means 133, 137 and 141
would be exposed to radiation. In FIG. 26, for operation as a
compressor chamber 591 would be exposed to radiation, especially
that part of it filled with liquid during operation.
In many applications, rotary inertial compressors are suitable as a
replacement for other forms of compressor. These can be used in
systems requiring distribution of compressed gas to operate other
equipment, such as pneumatic hammers, turbines, and the like; or as
part of a power plant, where the primary application is the local
conversion of the energy represented by the compressed gas into
mechanical work, electrical energy, or some other suitable form of
energy.
Combustion of fuel within the gaseous working fluid of a gaseous
compressor can be used either as a high-impedance source of thermal
energy, by holding the flow of fuel constant, or as a low-impedance
source, by utilizing control of the rate of flow of fuel to control
the rate of delivery of heat and thus maintain the temperature of
some point in the system essentially constant.
In the case of a nuclear reaction releasing energy within a
reaction zone in the working fluid, although the intrinsic heat
source impedance of a nuclear reaction is extremely high, the
physics associated with the way in which the reaction occurs, and
the way in which it feeds-back to sustain itself, can give rise to
a low impedance for the heat source. For instance, in a reaction in
which a moderator is used, an increase in temperature of the
moderator can reduce the reaction rate. In a reaction utilizing
just the gaseous component itself, an increase in reaction rate can
lead to an increase in temperature, expansion of the gaseous
working fluid, decrease in the total mass present within the
reaction zone, and decrease in the reaction rate. In these and
other ways, the temperature in the reaction zone can be held
relatively constant. This characteristic behavior is what one would
ordinarily associate with a low thermodynamic impedance heat
source. The flowing gases interact with mechanical and
thermodynamic impedances, both within the device and external to
it. This, again, illustrates the requirement that all of the
impedances in the entire system be taken into consideration in the
stabilization of a rotary inertial thermodynamic device.
LIQUEFACTION OF COMBUSTIBLE GASES
In devices using internal chemical reactions for heating, it is not
necessary that the gaseous fuel be completely burned. Thus, the
working fluid could be gaseous fuel with only a small amount of
oxidizer. Only a small portion of the fuel is oxidized, and the
remainder is used as the working fluid in the thermodynamic
process. FIG. 43 shows a compression device for liquifaction of a
combustible gas. The combustible gas (e.g., a mixture of gases,
such as natural gas) is introduced at 1060, and a suitable oxidizer
for reaction with the gas (e.g., air) is introduced at 1061. The
device 1062 is a rotary inertial thermodynamic gaseous compressor
to be operated on heat supplied by the reaction between the
combustible gas and the oxidizer. The device 1062 rotates on
bearings (not shown), and rotary seals 1064 form gas-tight seals
between the inlet and outlet conduits and the rotary conduit.
Reaction stabilization means 1063 is provided. The reaction (e.g.,
oxidation of a portion of the gas) occurs in region 1075.
Alternatively, the reaction stabilization means can use a catalyst,
especially when only a very small part of the gas is oxidized.
Also, the oxidizer can be guided separately to the reaction region,
and reacted in a suitable reaction chamber. This is directly
analogous to the introduction of fuel into an oxidizer stream, as
shown in the 51, by means of conduits 1103 and 1104. This is
helpful in that compressor 1062 can be used with an adiabatic
compression resulting in a high working fluid temperature, without
pre-ignition. Also introducing the oxidizer into a suitable
combustion chamber can facilitate more complete combustion, and a
more nearly stoichiometric reaction can be maintained. This can
reduce unwanted by-products otherwise often associated with
combustion int he presence of an excess of fuel compared to
oxidizer.
Gaseous working fluid leaves the rotating device in the direction
designated by arrow 1070. A first portion of the gas, under the
high pressure produced by the rotary device 1062, condenses in a
chamber 1076, giving up its heat of condensation to some external
heat sink through a thermodynamic impedance. This condensed working
fluid leaves the system through an exit port designated 1067, in
the direction of arrow 1072, through a suitable control means 9371.
In this way, many of the reaction products can be removed from the
combustible working fluid before it is further processed. An
uncondensed portion continues in the direction designated by arrow
1071 to a second chamber 1078, within which it condenses, giving up
its heat of condensation to some external heat sink through another
thermodynamic impedance. This condensed material then leaves the
system through outlet 1068, in the direction designated by arrow
1073, through an appropriate flow control means (valve) 1079. That
portion which is uncondensed leaves in the direction designated by
arrow 1074 through outlet 1069, fitted with appropriate control
means (e.g., a valve) 1080.
Consider, for example, the liquifaction of propane gas. This can be
accomplished by the introduction of a relatively small amount of
air through inlet 1061. The reaction between the propane and the
air would provide the heat necessary to operate the compression
cycle. Water from the reaction would condense in one chamber. The
propane would condense in the other chamber. The gaseous reaction
products from the combustion process would leave the system at
outlet 1069. In this way, relatively low contamination of the
processed gas could be achieved, while providing a relatively
economical way to accomplish the liquifaction desired.
In FIG. 44 is diagrammed a system for the fractional liquifaction
of combustible gases. Devices 1090 and 1095 are similar to device
1062 in FIG. 43. Following compressor 1090 are fractional
condensation chambers 1091 and 1093, similar to chambers 1076 and
1078 in FIG. 43. As many chambers as are needed may be used. These
operate at successively lower temperatures, separately condensing
progressively lower boiling fractions of the combined stream of
input gases and reactions products. After the lowest boiling
fraction which can be condensed at the temperatures and pressures
available has been extracted, the remaining stream enters a second
compressor 1095, and subsequent condensing chambers 1096 and 1098.
In compressor 1095, a small additional amount of oxidizer is
reacted with the combustible working fluid. Compressor 1095
multiplies the previous working fluid pressure by its compression
ratio. At the higher pressure resulting, lower boiling fractions
can condense in chambers 1096, 1098, etc.
Compression and fractional condensation means can be cascaded in
this way, to fractionate a large number of input gases, in a
relatively thermodynamically efficient manner. From the fractional
condensation means come streams 1092, 1094, 1097, 1099, etc. Some
of these may be reaction products, separated from the condensing
input gases, to be used or discarded. A final uncondensed portion
leaves as stream 1089, similar to that leaving through outlet 1069
in FIG. 43.
Systems of the foregoing type can utilize cascaded compression
stages in which partial combustion occurs in each stage, with
oxidizer and/or fuel being introduced in each successive stage. In
a device of the type shown in FIG. 43, stable operation requires
that the rotary inertial compressor be capable of supporting the
back pressure associated with the condensation processes and with
mechanical flow impedances in various conduits of the system. As
long as the amount of oxidizer is small compared to the amount or a
gaseous working fluid, the rate of introduction of the oxidizer
into the system determines the rate at which heat will be released
by combustion, almost independently of the rate of flow of the
combustible material itself, for a wide range of flow rates. By
utilizing this effect, the gaseous compressor can be made to have
wide range of effective delivery impedances for delivering working
fluid to subsequent portions of the system. Note that in gaseous
compressor 1062, the utilization of a single stage eliminates the
requirement for having a means for heat rejection from the rotating
device additional to the heat rejection provided by the exit from
the rotating device of warmed working fluid. If desired,
alternatively, each compressor could be a cascaded compressor of
the general type diagrammed in FIG. 51, with oxidizer being
distributed from inlet 1103, and combustible gaseous working fluid
entering at 1102 and leaving at 1115.
HEAT EXCHANGERS
The simplest heat exchange impedance and mechanical impedance
control means is a conduit. Such a conduit 891 is shown in FIG. 37.
Fluid flows through the conduit 891 in the direction 890. If the
conduit 891 has a large cross-sectional aperture 892 and short
length 893, the conduit has a low mechanical impedance to the flow
of working fluid and a relatively high thermodynamic impedance for
the tranfer of heat to or from the fluid. A conduit with a
relatively small cross-section 892, or a relatively long length
893, presents a substantially higher mechanical impedance to the
flow of working fluid, and a substantially lower thermodynamic
impedance to the flow of heat into and out of the working
fluid.
FIG. 38 shows an assembly 898 of parallel conduits 896 formed from
plates 894 separated by spacers 895. A device of this type can make
more effective contact, and, therefor, more effective heat exchange
with a fluid passing through it. The assembly 893 is a simple
extension of the form of conduit 891 of FIG. 37 and has essentially
the same properties as an assembly of such conduits in parallel. In
many instances such a conduit is a practical form of impedance
control means. An example of this will be given in greater detail
later.
In FIG. 39 is shown a heat exchanger and impedance control means
896 consisting of a parallel assembly of slender metal tubes 897
which are in contact with each other in a larger metal tube 899.
Heat is transferred to or from a fluid passing through the tubes
897 (in the direction 904) to the walls of the tubes and thence
through the wall of the outer tube 899 to its outside surface 903,
through which heat is exchanged with some other portion of a
system. Each conduit has a relatively very small inside
diameter
The device 896 is of a type which has been used as an intermediate
structure in the production of grids for klystron vacuum tubes. For
its use in impedance control, it should be noted that there is a
relationship between the optimum wall thickness of the tubes 897,
and the distance each tube 897 from outer tube 899. Those conduits
located near outer tube 899 conduct a larger amount of heat because
they conduct heat to or from conduits located deeper within the
impedance control device 897. For this reason, it is sometimes
preferred that the thickness of the walls of the conduits be
graded, increasing in thickness from within the device as the outer
wall 899 is approached.
Devices of the type shown in FIG. 39 are particularly advantageous
for providing impedances in an intermediate range, with a lower
thermodynamic impedance than typically is obtainable with a simple
construction using a few conduits of the type shown in FIG. 37, but
with a substantially higher mechanical flow impedance than is
obtained with such conduits. In a device of the type shown in FIG.
39, an appreciable portion of the total thermodynamic impedance of
the device can arise from the impedance to flow of heat caused by
the finite conductivity of the material of which the walls of the
conduit segments are made. The heat exchanger 896 can have a
cross-sectional shape other than cylindrical, if necessary. The
device 896 produces intimate contact over a relatively large
surface area between the metal of the tubes and the fluid flowing
through the tubes. The metal has a relatively high thermal
conductivity.
FIG. 40 shows another form of impedance control means, consisting
of a sintered metal porous plug or body 905, or other porous, high
thermal conductivity material, such as beryllia. Working fluid
flows through the pores of this material and exchanges heat with it
and with its outside surface 906. In such an impedance control
means, the bulk of the thermodynamic impedance for transfer of heat
between a flowing working fluid and the surface 906 arises from the
thermal conductivity of the porous material, rather than from the
exchange of heat between the working fluid and the porous material.
The working fluid is in intimate contact with the porous material.
For this reason, heat exchange between fluid and exchange means can
be effectively accomplished with a relatively short length 907.
An alternative way to use an impedance control means of this type
for exchanging heat with the working fluid is to utilize some form
of energy transport means which results in heating of the porous
material. For example, this type of impedance control means is
particularly advantageous when heat is to be transferred by
electromagnetic induction, in which the heat can be caused to
develop within the material itself, without requiring that heat be
exchanged with the external surface 906. In that case, there is no
appreciable thermal impedance arising from the thermal conductivity
of the material of which the plug is made.
In FIG. 40 are also shown two optional electrodes 916 and 917
connected to opposite faces 914 and 915 of the body 905. By
utilizing an appropriate electrically conductive material as the
porous material, the thermal energy can be released with the body
905 directly by passing an electric current therethrough. This form
of heating is particularly advantageous when the impedance control
means has a short length 907 in the direction 918 of flow of the
working fluid. The advantage arises from the elimination of any
effect due to the thermal impedance associated with the finite
conductivity of the porous material of which the device 905 is
made. This allows the use of quite short impedance control means
while still retaining effective exchange of thermal energy to feed
heat into the working fluid passing therethrough. Thus, the device
905 with its electrodes can be used as the means 910 for converting
electrical energy into heat energy in the rotary device shown in
FIG. 36.
Several peculiarities in the operation of rotary inertial
thermodynamic gaseous compessors are worth noting. First, gaseous
working fluid near the axis is often at a much lower pressure and
much lower density than working fluid near the periphery of the
rotating device. The mass flow passing any point in a single
conduit is constant after the initial fluctuations of start-up
decay to the steady state operating value. For this reason, the
velocity of working fluid for the same cross-sectional area of duct
increases with decreasing radius, corresponding to the decrease in
density of the working fluid as it approaches the axis. For this
reason, impedance control means used near the axis should be
designed for a relatively larger volume of flow than impedance
control means used far from the axis of rotation, although in both
cases the mass flow is the same.
Another effect of the smooth change in pressure with radius is that
if an acoustic wave occurs in the gas, and if that wave represents
a certain fraction of the total pressure near the axis, it
represents a steadily decreasing fraction of the total pressure of
the gaseous working fluid as the distance from the axis is
increased. Conversely, an acoustic wave near the periphery in the
working fluid represents a progressively larger fraction of the
total pressure of the working fluid at it approaches the axis. This
can lead to a small acoustic wave near the periphery giving rise to
a shock wave near the axis.
Acoustic waves can be produced within the conduits of a gaseous
system by many well known effects, such as vortex shedding,
oscillation over an aperture, and oscillations resonant with some
structure in the device. In addition to these gas dynamic effects,
there are also effects which arise from the interaction of these
gas dynamic properties with the thermodynamic impedances within the
system. For instance, the effectiveness of a heat exchange means
may be influenced by the onset of vortex shedding within it. This
can cause the temperature of the heat exchange means to change,
which in turn affects the presence or absence of the vortex
shedding phenomenon within it, and its effectiveness in producing
heat exchange with the working fluid, which, in turn, affects the
temperature, the density, and the effect of centrifugal forces upon
the working fluid. Variation in the effects of density and
centrifugal forces, in turn, can give rise to variations in the
effective compression or expansion in the working fluid produced by
the rotary inertial thermodynamic effects, thus giving rise to
changes in the flow velocity, which in turn feed back to affect the
vortex phenomenon. All of the foregoing phenomena have associated
with them various time delays, depending upon the nature of the
materials, the geometry of the device, flow velocities, angular
velocity of rotation, and other variables of the system. For this
reason, the detailed analysis of the behavior of a pulse of
pressure or temperature introduced within a rotary inertial
thermodynamic system can be quite intricate. However, many of the
important stability properties of rotary inertial thermodynamic
systems can be understood in terms of relatively slow effects,
which occur at a rate which is slow compared to the time required
for the adjustment of internal temperatures and the propagation of
internal pressure waves. These steady-state analyses lead to a
fairly detailed and consistent set of conditions under which rotary
inertial thermodynamic systems can operate stably. The relations
required for these analyses are subject to experiemental
measurement. Typically, the relations involve the pressure drop as
a working fluid passes through a rotary inertial thermodynamic
device, and the rate of flow of the working fluid through it. This
relationship, in turn, is effected by thermodynamic and mechanical
impedances of the entire system, of which the device is a part.
These relations give rise to criteria for stability for systems
operating in an essentially steady state condition, that is,
operating with flow rates which are essentially independent of time
over periods of time comparable to the time required for an
acoustic impulse to propagate through the working fluid through the
length of a typical conduit within the system.
Another effect is that, in the evolution of a gas from a liquid,
within a rotary inertial thermodynamic system, the strong
dependence of local pressure within the fluid upon distance from
the axis of rotation gives rise to fairly well defined radii at
which gas evolution begins to occur, depending upon the temperature
and nature of the working fluids involved.
The availability of working fluids at various pressures within the
rotating devices makes it possible to utilize fluidic control and
amplification systems formed within the rotating member itself. In
this way, the response of such systems to temperature and pressure
differences and flow rates can be made almost arbitrarily intricate
to suit specific applications. However, control means of this type
ultimately have the effect of controlling the effective impedance
presented by the rotating device, and/or by other parts of the
system of which it is a portion. The overall performance and
stability of such systems can be understood in terms of the
requirements on the impedance for small fluctuations about a
selected operating point. If this impedance is positive then
operation at that point can be stable. If it is negative, then, in
general, operation at that point will not be stable. That is,
elaboration of the control means beyond those arising simply from
the thermodynamic impedances and mechanical impedances within the
devices themselves, does not change the basic nature of the
stability requirements.
Non-Combustible Gas Liquefaction
FIG. 46 shows a rotary inertial thermodynamic cooling device 1029
which is capable of cooling substances to extreme low tempertures,
and is particularly useful in liquefying air, hydrogen, etc. The
device 1029 has a single closed loop circuit of the type shown in
my U.S. Pat. No. 3,470,704. In this device section 1036 acts as a
gaseous compressor of a type discussed previously. In region 1037
heat is rejected through impedance Z1032 to an external
environment. Region 1038 is a countercurrent heat exchanger of the
type illustrated in FIG. 9 of my above-identified patent which
conducts heat from conduit segment 1040 to conduit segment 1041
through impedance Z1033. Region 1039 represents a cooling section
in which working fluid progresses radially inwardly through conduit
segment 1034. In doing so it expands, achieving a lower temperature
than that which it had in conduit segment 1040. This
lower-temperature working fluid then progresses through conduit
segment 1041 in the direction designated by arrow 1043. As it moves
within conduit segment 1041, it absorbs heat through thermodynamic
impedance Z1033 from working fluid in conduit segment 1040. In this
way, a regenerative cooling effect is produced, so that the
temperature achieved near the axis of rotation in conduit segment
1034 can be quite low. This can then absorb heat from some external
source (e.g., a gas to be liquified) through an impedance Z1035,
producing cooling. Because working fluid in conduit segment 1034
during normal operation is quite cold, it has a substantially
higher density than would be achieved if it were simply utilized in
a device without the regenerative heat exchange means Z1033. This
results in a substantially greater back-pressure associated with
the action of rotational inertial forces upon the mass within
conduit segment 1034. This allows the portions 1037, 1038 and 1039
of the device to sustain a relatively large forward pressure
driving working fluid through it.
The flow of working fluid within this device 1029 depends upon
impedances for heat transfer, as well as internal mechanical
impedances. Not only the internal impedance Z1033 by which the
countercurrent heat exchange is accomplished, but also external
impedances Z1035, Z1032 and Z1031 participate in determining the
stability of operation. In particular, if Z1031 is large, then the
heat source has a high characteristic impedance, and, therefore,
the flow output impedance of compressor 1036 is relatively high,
thereby satisfying the requirements for stable operation of a
device of this type, as discussed in greater detail previously.
Although for specificity 1036 is shown as being a single-stage
rotary inertial thermodynamic gaseous compressor, it is to be
understood that as many stages as needed can be used to provide the
relatively high drive pressures required.
Suitable impedance control means within the various segments of
conduit participate in forming the overall impedances, and
participate in providing for stable flow of working fluid.
One way to achieve the thermodynamic coupling represented by
impedance means Z1033 is to utilize a gas freely moving between the
tube sections 1040 and 1041 and carrying head by convection as
indicated by the arrows 1081. The gas chosen should have relatively
low molecular weight so that the effects of compression upon it are
not as great as the effects of compression on the working fluid
which is producing the primary cooling effect. For this reason,
hydrogen and helium would be suitable gases for use as the heat
transfer gas. Other possible heat transfer means, in addition to
conduction and convection, include evaporative heat transfer.
FIG. 47 is a schematic diagram of a system for the liquefication of
gases, comprising a compressor 1044, a cooler 1046, and heat
exchange means 1045. All of these can be combined in a single
rotating device as shown in FIG. 48. The device shown in FIG. 48
includes a multiple-branch cascaded gaseous compressor 1048,
bearing in a single cascaded compression rotor at least two
entirely separate branches. One branch serves as a compressor for
the gas to be liquefied (taken in at an inlet 1047), and another
branch serves as a compressor to actuate a regenerative
counter-current cooling device 1049 of the type shown in FIG. 46.
The gas to be liquefied flows into the inlet 1047, is compressed in
the compressor 1048, and flows through a conduit 1050 along the
axis 1. The gas in conduit 1050 gives up its heat by
counter-current heat exchange to the very cold gas in conduit 1046
of the cooler, and exits through an expansion valve 1051 and an
outlet 1052. In this way an appreciable fraction of the gas is
liquefied. This device illustrates the use of several disjoint
branches of a thermodynamic system which are physically part of the
same device. Arrows 4762 and 4733 indicate which inlets of the
compressor are connected to which outlets.
One of the reasons for wanting to operate several branches of a
rotary inertial thermodynamic gaseous compressor in parallel is to
allow symmetrization of the device with respect to the axis of
rotation. A second purpose is to allow cascaded compressor stages
to be utilized in a symmetric fashion so that as working fluid
pressure builds up towards the latter stages of the device, a
rotational imbalance will not be caused by the additional mass of
working fluid accumulated in the latter stages of the device. Many
different branches can be interleaved with each other.
STAGGER-WOUND HELICAL COMPRESSOR
FIG. 49 shows a single-branch cascaded gaseous compressor 820 whose
stages are made nearly symmetrical about the axis of rotation by
using a larger angular increment betweeen successive stages than
the number of stages would require to fit in a single turn about
the axis of rotation. In this way the stages loop about the axis of
rotation many times. In FIG. 49, 1 is the axis of rotation, and 822
and 823 are connections from the rotary inertial thermodynamic
cascaded gaseous compressor to other devices within the system.
There are six compression stages 824. The stages are interleaved so
that in three stages the conduit has gone completely around the
axis of rotation. 825 generally designates a rotary structure
supporting the stages. FIG. 49 is schematic, intended solely to
represent the angular increments between the stages and the way in
which they overlap. The angle between two successive stages is
designated 826. The angular increment necessary to make the stages
fit in a single pass around the axis of rotation is designated 827.
Here there is a twofold interleaving represented by angle 826 being
approximately twice angle 827.
PARALLEL-CASCADED HEAT-PUMPS
FIG. 50 shows a rotary inertial thermodynamic device 1050 utilizing
a gaseous compressor 1053 comprising several separate branches,
each containing several stages of compression in cascade. These are
utilized to operate separate cooling devices 1057 and 1058. Device
1057 rejects heat through impedance Z1054 to some external
environment. Device 1058 rejects heat through impedance Z1055 back
to device 1057. Device 1058 absorbs heat from some external source
through an impedance Z1056, thereby producing a cooling effect. By
utilizing a series of two or more cooling devices in this way, with
thermodynamic impedances internal to the rotating device coupling
the cooling devices to each other, the whole device 1060 will be
capable of producing an extremely large temperature differential.
Various different working fluids can be used in the separate
cooling devices, with the working fluids being appropriate to the
various temperatures at which heat is absorbed and rejected by each
of the cooling devices. Arrows 4734, 4735, and 4736 indicate which
inlets of the compressor are connected to which outlets.
The device 1060 has the capability of extracting heat from a load
to be cooled which has, in effect, a relatively high thermodynamic
impedance to heat flow; that is, from a load which makes it
necessary to extract heat at a very low temperature. Also, heat can
be extracted from low impedance sources which have a characteristic
temperature which is intrinsically quite low, for example, in the
liquefaction of gases.
In order to liquefy gases (e.g., air), an inlet 1047, tube 1050,
and a valve 1051 carry the gas to be liquefied, in the same manner
as in FIG. 48. The gas in tube 1050 gives up its heat to the
liquids in the evaporators of the coolers (as is indicated by the
dashed arrows) to cool the gas to extremely low temperatures.
Heating for the coolers 1057 and 1058 can be by any of the means
disclosed herein. For example, such a device could be heated by
combustion. A system utilizing a heat source based on combustion
and a liquefaction scheme of this type could be especially useful
for the liquefaction of combustible gases, such as natural gas, and
of air.
Although it is generally desirable that the temperature of
operation of a rotary inertial gaseous compressor using combustion
within its working fluid be high enough so as to insure that the
combustion products remain in gaseous form, and not accumulate
within the device, it is possible to provide discharge means such
as a trap 1083 (FIG. 43), for the elimination of such combustion
products in the event that they do tend to accumulate. Utilization
of such a mechanism is optional. For example, where powdered coal
is used as the fuel, molten slag will be removed through the trap
1083. For some applications, it may be desirable to operate device
1062 in a vacuum chamber (not shown) for greater efficiency.
CASCADED COMPRESSOR WITH INTERNAL FUEL OXIDATION
FIG. 51 shows a cascaded gaseous compressor utilizing combustion
within the successive stages to provide the heat necessary for
their operation. Axis of rotation is designated 1. Through inlet
1101 is taken in a working fluid 1102 which can support combustion.
It is assumed for specificity that this working fluid is an
oxidizer, and that the reactant with it will be a fuel. This fuel
enters at inlet 1103 to distribution system 1114. Fuel flows
radially outwardly through conduit means 1104, a preheater 1106,
and then through outlet 1112, to mix with oxidizer and enter the
combustion area through stabilizing means 1105. Reactants from this
combustion and unburned oxidizer progress radially inward through
conduit segment 1118, then proceed radially outward through heat
exchange means 1108, which couples heat from the heated working
fluid to some external heat sink, with a total effective
thermodynamic impedance Z1107. Fuel conduit segment 1109, preheater
1110, orifice 1113 and combustion stabilizer 1111, operate in the
same way as their corresponding components in the first stage.
Optional drains 1116 and 1117 are provided, if desired, for
removing reactants which tend to accumulate in the system. Working
fluid leaves the system through outlet 1115 in the direction
designated by arrow 1119.
Except for the means by which heat is introduced into the working
fluid, the cascaded gaseous compressor in FIG. 51 is essentially
similar in operation to that in FIG. 10, with the exception that
the introduction of heat into the working fluid is not necessarily
isothermal, because of the nature of combustion. The impedance
Z1120 and associated heat exchanger 1121 can be provided in conduit
segment 1122 in the event that the inlet working fluid is already
at a temperature roughly near that at which heat is to be rejected.
(In FIG. 10 it is assumed that the working fluid enters the system
at a relatively low temperature.) There are several reasons for
utilizing partial combustion in each stage of compression. In a
practical system, the maximum temperature which can be achieved in
the rotating device is limited by the properties of materials and
by the angular velocities available. For this reason, it may not be
feasible to operate a full combustion Carnot cycle in a single
stage. However, several cascaded stages of compression can each,
separately, approximate fairly closely a Carnot cycle by utilizing
heat rejection through impedances Z1120 and Z1107, such that the
combustion, when it occurs, leads to a rise in temperature of a
magnitude which, after adiabatic expansion in conduit segments
radially inward from the combustion zone, has reduced the
temperature of working gases, and allows essentially isothermal
heat rejection to occur. It is within present materials technology
to achieve, in this way, a Carnot cycle efficiency in excess of 50
percent. The maximum temperatures occurring in a Carnot cycle with
an efficiency of 50 percent and heat rejection temperature of 400
degrees Kelvin are substantially lower than the maximum
temperatures which would be produced by total reaction of, for
example, air with a typical hydrocarbon fuel, such as gasoline or
propane. This use of successive stages with combustion allows the
maximum temperature to be held to a low enough value to be feasible
with currently available materials, and also helps to insure
complete combustion of the smaller amount of fuel used in each
stage, thereby reducing the production of undesirable
byproducts.
Means for providing rotation, bearings for support, and rotary
seals for feeding in working fluid and fuel, and for receiving
working fluid from the outlet of the device, have, for simplicity,
not been shown. A gaseous compressor utilizing combustion or other
reaction within its working fluid can be used, not only to provide
its own operating heat, but also to provide operating heat for
other rotating devices through appropriate thermodynamic
impedances. In FIG. 51, as well as other systems disclosed herein
utilizing combustion for heating, appropriate means for initiating
such combustion are included if necessary in the combustion area
(inwardly from the combustion stabilizer). However, in most of the
drawings herein, these ignition mechanisms have not been shown for
the sake of simplicity. In some cases, heat of compression can
provide ignition, as in a diesel engine.
ABSORPTIVE ROTARY THERMODYNAMIC COMPRESSOR
FIG. 52 is a diagram of an absorption cycle rotary inertial
thermodynamic compressor in which an absorbent fluid component
circulates entirely within the rotary inertial thermodynamic
device, and a gaseous component is absorbed from outside the device
and delivered to outside the device, either to other components of
a system which rotate with it, or are stationary. Working fluids
for use in this embodiment include the following well known pairs:
(a) water and ammonia, with ammonia vapor as the gas; (b) a water
solution of lithium bromide, with water vapor as the gas; and (c) a
water solution of lithium iodide, with water vapor as the gas. Of
course, other known pairs also can be used.
Gaseous working fluid flows into the system at inlet 672 in a
direction designated by arrow 670. It enters chamber 673, where it
contacts absorbing fluid 674 at surface 687, and is absorbed
thereby. This combination of absorbing fluid and the absorbed
gaseous component which had entered the system moves radially
outward through conduit section 676 in the direction designated by
arrow 675, passing through a rotary inertial trap 691, into a
chamber 679. Chamber 679 is supplied with heat from a heat source
678 through impedance Z677. Impedance Z677 represents the total
impedance for heat flow into working fluid within chamber 679,
including that part of the impedance which is external, and that
part which is internal, to the chamber. Gaseous form working fluid
is evolved from working fluid solution 680 in chamber 679, and
proceeds as a set of alternating slugs of liquid and gas, radially
inward in a direction designated by arrow 682 through a lift tube
683, exiting from the lift tube 683 at outlet 684 in chamber 685.
In chamber 685, the liquid and gaseous components exiting at exit
684 are separated, with liquid components leaving chamber 685 and
flowing radially outward and into conduit segment 689. Gaseous
working fluid leaves chamber 685 through the outlet of the rotary
inertial thermodynamic compression device 690, in the direction
designated by arrow 671. Gaseous form working fluid in chamber 685
is at a higher pressure than in chamber 673. For this reason,
liquid working fluid, exiting chamber 685, flows radially outward
to a surface 686 in conduit segment 689 which is, radially further
outward than surface 687 in chamber 673. This difference in radial
position is designated by numeral 688.
Conduit segment 689 forms a rotary inertial trap, within which
liquid working fluid flows in the direction designated by arrow
692. Liquid working fluid exits from conduit segment 689 into
chamber 673, and flows therein, absorbing gaseous working fluid and
leaving therefrom through conduit 676, continuing the cycle. In
this way, liquid working fluid, acting as an absorber, flows in a
closed cycle within the rotary inertial thermodynamic device shown
in FIG. 52, and gaseous working fluid flows through it in a single
pass, entering at 672 and leaving at 690. Conduit segment 676, trap
691, chamber 679 and lift tube 683 together comprise a "lift tube"
type of compressor which is disclosed in my co-pending U.S. patent
application Ser. No. 843,167, filed July 18, 1969, now U.S. Pat.
No. 3,559,419, issued Feb. 2, 1971. This subsystem has a maximum
pressure into which it can deliver liquid and gaseous working fluid
at the exit of lift tube 684 in diagram 52. Also, there is a
maximum pressure which can be supported across rotary inertial trap
means 689, considered together with liquid form working fluid level
687 in chamber 673. Whichever of these pressure differences is
smaller determines the maximum pressure at which gaseous form
working fluid can be delivered at exit 690.
Depending on the nature of the combinations of working fluids used
within this system, chamber 673 may or may not be required to
dissipate heat. In the event that it is required to dissipate heat
it is coupled to the external environment through a thermodynamic
impedance designated Z693. Z693 is used here to designate both
internal and external thermodynamic impedances associated with the
flow of heat from working fluids in chamber 673.
FIG. 53 shows two types of relationship between pressure and flow,
for a device of the general form in FIG. 52, depending on whether
the limitations on maximum pressure arise from the failure of the
trap 689 to support pressure, or failure of the lift tube assembly
to deliver working fluid at pressure. Both have in common line
segment 695, representing compression under normal operation, with
the delivery of gaseous form working fluid in the direction
designated by arrow 671 at outlet 690. In the event that the
limitation upon the maximum pressure difference which can be
delivered between outlet 690 and inlet 672 is determined by failure
of trap 689, the forward pressure near zero flow is nearly
constant, with output pressure depicted by line segment 4740, and
reverse flow is represented by line segment 696. In the event that
trap 689 can support a back pressure larger than that into which
the lift tube subsystem can deliver liquid and gaseous working
fluid, forward compression at nearly zero flow has a form indicated
by line segment 4741, and there is a gap, designated 698 in FIG.
52, after forward flow has ceased and before reverse flow begins.
In that case, reverse flow follows the line segment 697. The
maximum back pressure occurring at the onset of reverse flow
designated 699, will depend on which of the two portions of the
device fails in the reverse mode at lower pressure. It could be by
back-flow through trap 689, or it could be by back flow through
trap 691. In the figure as drawn, the back flow would occur through
trap 689. The two different ways in which the maximum pressure can
arise give rise to pressure flow relationships which have in common
a stable operating forward compression segment 695. However, branch
696 begins at the intercept of branch 4740 with the zero flow axis.
For this reason, if several parallel branches were utilized with a
system having that type of limitation, small variations in geometry
or thermodynamic impedance within each of the branches could give
rise to slightly different pressures such that, as the total
paralleled flow approached zero, one of the branches could be
forced into reverse flow. In the case where the relationship
between back pressure which can be supported by trap 689 and the
maximum forward working pressure delivered by the lift tube
subassembly is such that there is a gap 698, this gap makes a set
of parallel branches act in an unconditionally stable manner, i.e.,
if the system is operated into a closed vessel so that it delivers
gaseous working fluid at the maximum pressure which it can produce,
there is no tendency for the flow of working fluid to reverse in
any one of the branches.
It should be noted with regard to the operation of any of the
rotary inertial traps, e.g. 689 or 691, that if the tube, in this
case conduit segment 689 or conduit segment 676, has two small a
diameter, it is possible for a gaseous form of working fluid to
drive ahead of it liquid form working fluid, and empty the trap.
That would give rise to a reverse flow characteristic more nearly
like that designated by line segment 700 in FIG. 49. The
requirement for normal trap operation is that the gaseous form
working fluid be able to form bubbles which move relative to the
liquid form working fluids, so that the liquid continues to remain
in the trap, that is, the minimum tube diameter is appreciably
greater than the expected bubble diameter. Because of the
centrifugal forces acting on the liquid form working fluid this
requirement is relatively easily satisfied.
In an absorptive cycle system it is often desirable to provide for
heating a fluid to drive off absorbed working fluid, in addition to
that heating which is utilized in evolving gases to operate a lift
tube. Provision is made for this in FIG. 52 by the option of adding
a small dam 850 extending radially inward from outer surface 853 of
chamber 685. This dam, if used, provides space for the
accumulation, against outermost wall 853, of absorbent fluid 852,
in which location it can readily be heated through impedance source
Z851 by a heat source 854. This heat source may be the same as
source 678. Use of such an additional space for additional heating
is optional. With some working fluids under some operating
circumstances it is desirable, with others for specific
applications it is not necessary. Heat exchanges among various
flows within the device have not been shown, for simplicity.
CASCADED ABSORPTIVE AND GASEOUS COMPRESSORS
It is feasible to connect several different forms of rotary
inertial thermodynamic compressor in cascade. For instance, an
absorption type compressor of the form shown in FIG. 52 could be
used to deliver gaseous working fluid into a cascaded gaseous
rotary inertial thermodynamic compressor. The heat flow through the
two compression units could also be in series, with heat being
delivered initially to the cascaded gaseous compressor and its
waste heat being utilized as the actuating heat designated heat
source 678 in FIG. 52, for the absorptive type compressor. Such a
combination is particularly advantageous where gaseous form working
fluid must be taken in at a relatively low pressure. The absorptive
type compressor would serve to produce an initial compression,
after which the gaseous compressor is fed at a relatively high
intake pressure. The gaseous rotary inertial thermodynamic
compressor operates to multiply the input pressure by a factor,
depending upon its impedances and operating points. By utilizing a
precompressor, it is possible to shift the operating points of the
cascaded gaseous compressor so as to obtain the overall compression
desired with a smaller number of stages. Such a combination offers
a higher overall thermodynamic efficiency, where a very large ratio
of outlet to intake pressure is required, than might be readily
achieved by a gaseous unit alone. Utilization of such a cascaded
system allows an extremely low mechanical intake impedance to be
realized in a thermodynamically efficient manner. Furthermore,
where parallel branches are desired, the utilization of such a
cascade allows one of the devices to provide the stabilizing
pressure flow relationship for the other device, so as to make the
entire branch unconditionally stable. Thus, it is possible to
construct multiple branch systems, utilizing several different
forms of compressor in each branch, and, if desired, utilizing
different forms of compressor in different branches, such as
cascaded gaseous compressor in one branch, an absorption type
compressor in another branch, a liquid-gas compression cycle in a
third branch, etc., or combinations of these or others in any
single branch. As long as the impedance requirements and the
pressure flow relationships are satisfied, the operation of such a
system will be stable. By choosing proper combinations, or by
utilizing additional constraints, such as a simple valve assembly,
it is possible to make the operation of such systems
unconditionally stable over very wide operating ranges.
One of the advantages of the absorptive type system in which the
absorbent follows a closed cycle and the gaseous component is part
of an open cycle, is that it is possible to achieve a very large
volume of intake with a high compression ratio in a compact device.
For example, if water vapor is the gaseous component and a salt
solution of lithium bromide with water or lithium iodide with water
is the absorbent, a device with a diameter of only a few inches
spinning at 1000 rpm to 3000 rpm is capable of handling a
substantial volume of intake and providing a pressure differential
in excess of 300 mm mercury. Potential applications for such a
device include freeze-drying of foods, as well as refrigeration and
air conditioning. Systems of this type can be scaled down to a
quite small diameter or up to relatively large diameters depending
on the nature of the working fluids, pressure differentials, and
pumping capacities required.
COUNTER-CURRENT HEAT EXCHANGE: ABSORPTIVE HEAT PUMP
In absorption cycle cooling units, the maximum thermodynamic
efficiency available is determined partly by the maximum
temperature at which heat can be accepted from the actuating heat
source. In such devices, the chemistry of the absorption process
imposes temperature and efficiency limitations on single stage
configurations. For absorbent and gaseous working fluid
combinations in which the absorption of the gaseous form of working
fluid results in the evolution of heat, this limitation can be
substantially ameliorated through the use of a counter-current heat
exchange system in which part of the heat evolved during absorption
of gaseous working fluid is utilized in providing the heat
necessary for the evolution of gaseous working fluid in a different
part of the system. In FIG. 56 is shown a system 1400 utilizing
this principle.
In the system 1400, the absorption of vapor form working fluid by a
relatively concentrated absorber is allowed to occur at a high
temperature, so that the heat evolved therefrom can be utilized to
heat an absorbent at a somewhat lower temperature and lower
concentration to evolve gaseous working fluid therefrom. In FIG.
56, two extended chambers, 1435 and 1438, are utilized in
conjunction with extended heat transfer impedance means Z1405 to
form a counter-current heat exchanger. Thermodynamic impedances
Z1405 convey heat from liquid working fluid absorber, or `liquor`,
1414, progressing in the direction of arrow 1416 within chamber
1435, to the liquors 1415 progressing in the direction of arrow
1417 in chamber 1438. In so doing, they allow liquor to exchange
heat in the necessary counter-current fashion. Gaseous working
fluid is evolved within chamber 1438 from liquor 1415. This gaseous
working fluid 1439 travels in the direction of arrow 1573, giving
up heat to liquor 1415 through distributed impedance Z1575 in
counter-current fashion, leaving chamber 1438 at outlet 1576,
proceeding through conduit 1426 in the direction of arrow 1433 into
counter-current heat exchanger 1571, characterized by distributed
thermodynamic impedance Z1570, in which it exchanges heat with cold
vapor from chamber 1431 and may partially condense, thence into
condensing chamber 1427, wherein condensation is completed, giving
up its heat of condensation to an external heat sink through an
overall thermodynamic impedance Z1409, representing internal and
external heat-exchanger impedances. This condensate leaves
condenser 1427 through outlet 1428 into conduit 1429, containing,
if desired, an appropriate flow control means Z1410. This flow
control means has a mechanical impedance and can, for example, be
of the form of one of the self-adjusting impedances discussed
earlier.
From conduit 1429 condensate 1430 progresses into chamber 1431,
wherein it evaporates at reduced pressure, absorbing heat from an
external heat source through an overall thermodynamic impedance
Z1411. This is the process by which heat is moved from the source
supplying heat through Z1411 to the sink absorbing heat rejected
through Z1409. Low pressure vapor-form working fluid progresses
through conduit 1432 in direction of arrow 1434 into chamber 1435.
This vapor form working fluid 1436 is then absorbed by liquor 1414.
As the liquor progresses from inlet 1425 through chamber 1435 to
outlet 1419, it becomes progressively more dilute. At the same
time, its temperature decreases. The relationship between
temperature, concentration of absorbent, and vapor pressure is
utilized in this way in that the temperature is reduced so that the
absorption of vapor-form working fluid 1436 by absorber 1414
proceeds with only small deviations from thermodynamic equilibrium
as the absorber progresses through chamber 1435. In the regions
between dotted lines 1404 and 1406, the concentration of the
absorber is high enough so that the absorption of low pressure
vapor occurs at a temperature higher than will be required for
evolving higher pressure vapor in chamber 1438 from a more dilute
solution of the absorber.
Because the evolution of gaseous working fluid 1439 in chamber
1438k must occur at a higher pressure than that present in chamber
1435, in order to provide the pressure necessary for condensation
in chamber 1427 and rejection of heat through impedance Z1409, the
relationship between temperature, concentration of absorber, and
vapor pressure requires that the temperature of the solution be
higher in order to evolve vapor form working fluid, for any given
absorber concentration, in chamber 1438 than in chamber 1436. The
higher temperature required to evolve vapor in chamber 1438 for a
given liquor concentration means that there exists a maximum degree
of dilution of absorber 1414 in chamber 1435 above which further
dilution by absorption of gaseous working fluid cannot occur in an
equilibrium fashion at a temperature high enough to actuate the
evolution of vapor from any of the working fluid present in chamber
1438. From this point, designated by dotted line 1406, to the end
of chamber 1435, all additional absorption of vapor form working
fluid occurs with the rejection of heat of absorption through an
impedance Z1407 to some suitable heat sink. The further diluted
absorber 1414 then leaves chamber 1435 at outlet 1419, through
conduit 1420 containing flow control impedance 1412, and into
chamber 1438 at inlet 1421. The dilute absorbent entering chamber
1438 at inlet 1421 progresses in the direction of arrow 1417. This
liquor 1415 gradually evolves vapor 1439 as it absorbs heat
transferred into it through thermodynamic impedances Z1405 and
Z1575. The heat transferred through Z1405 is released in chamber
1435 by the absorption of a lower pressure vapor by a more
concentrated absorbent. It is this portion of the process,
occurring in chamber 1438 between inlet 1421 and dotted line 1404,
that accounts for the increased efficiency of a system of this
type.
As liquor 1415 progresses in direction 1417 through chamber 1438,
its concentration is gradually increased as it evolves vapor. As
this occurs, its temperature also is gradually increased to allow
the continued evolution of vapor in a nearly equilibrium manner.
However, as the concentration of the absorber increases, it reaches
a concentration above which no temperature appearing in chamber
1435 is sufficiently great to allow evolution of vapor 1439 at the
higher pressure appearing in chamber 1438. In the region in chamber
1438 between dotted line 1404 and outlet 1422, the absorber is more
concentrated than this value. In this region, further evolution of
vapor is actuated by heat transferred from heat source 1403 through
thermodynamic impedance Z1402 into absorber (liquor) 1415.
This thermodynamic process of counter-current absorption and
re-evolution of vapor form working fluid allows the process to be
tailored to a wide range of temperature differences between
condensor 1427 and evaporator 1431. As the temperature difference
between evaporator and condensor is made smaller, the vapor
pressure difference is also made smaller, so that the vapor
pressures in chambers 1435 and 1438 become more nearly equal. This
allows a progressively larger fraction of the total heat exchanger
process, occurring with absorption of vapor in chamber 1435 and
evolution of vapor in chamber 1438, to be accomplished through the
exchange of heat between the two chambers, utilizing impedances
Z1405. At the same time, a smaller amount of heat input through
impedance Z1402 and heat rejection through impedance Z1407
accompanies the total flow of heat between the two chambers. In
this way, the overall heat pumping ratio, that is, the heat
transferred (taken in through impedance Z1411 and rejected through
impedance Z1409), divided by the heat taken in through impedance
Z1402 from heat source 1403, becomes larger, the smaller the
temperature difference between the evaporator and condensor.
After it has reached the maximum concentration desired in the
thermodynamic process, absorber 1415 leaves chamber 1438 through
outlet 1422, proceeds through conduit 1423 through pump means
P1413, thence in direction of arrow 1440 through conduit 1424, to
reenter chamber 1435 at inlet 1425. Impedance Z1441 of impedances
Z1405 represents thermal coupling between fluid flowing in conduit
1424 and liquid 1415 in chamber 1438. This allows for the
precooling of high temperature absorbent before it enters chamber
1435. FIG. 56 is intended as a schematic system diagram to
facilitate the explanation of the thermodynamic processes occurring
therein.
It is to be understood that pump means P1413 and flow control means
Z1412, can be located at suitable places within the system. For
example, the region of chamber 1438 between dotted line 1404 and
outlet 1422, and pump means P1413, can be replaced partially or in
their entirety by a lift tube assembly, utilized to provide both
additional heating and the desired pumping. Alternatively, chamber
1438 could be divided at location 1404 to allow a lift tube
mechanism to be placed between the two portions resulting of
chamber 1438. This would be a particularly advantageous location
for a lift tube, because the absorbent 1415 has not yet been
concentrated so greatly as to make the amount of vapor form working
fluid, yet to be evolved, so small as to render relatively
ineffective the operation of a lift tube transport system.
The closed cycle process depicted in FIG. 56 can be opened at
locations 1443 and 1442 to provide an open cycle system with
respect to the flow of the absorbed vapor, and a closed cycle
system with respect to the flow of the absorbent, in much the same
way as was done with the device in FIG. 52.
It is to be understood that use of a buffer gas, where appropriate,
is compatible with the counter-current heat exchange process set
forth in FIG. 56. With some combinations, use of a buffer gas is
well known, e.g. use of hydrogen as a buffer with water as the
absorber and ammonia as the vapor.
FIG. 57 shows the structure of a rotary inertial thermodynamic
embodiment utilizing the system shown in FIG. 56. For the sake of
simplicity, the various conduits in FIG. 57 have been shown as if
they lay essentially in a single plane parallel to the axis of the
rotating device. Actually, however, this is not usually true.
Each of the chambers 1458, 1461, 1470, 1469, 1478, 1475 and 1473
extends entirely around the axis of rotation 1 as a figure of
revolution, having as cross-section the cross-section shown in FIG.
57. In each chamber except chamber 1473, a dam stretches across
each chamber parallel to the axis and extending radially inwardly
from the outermost surface of the chamber in to a point closer to
the axis 1 than the surface of the liquid contained within that
chamber during operation. These dams are not shown in FIG. 57.
However, when liquid is fed into one of the chambers, for example,
chamber 1469 at inlet 1486, it is to be understood that the entry
to the chamber is near the dam on one face thereof, and that the
exit 1485 is near the dam on the other face. In this way, liquid
working fluid is forced to flow around the circumference of the
chamber so as to spend the maximum distance within the chamber.
FIG. 58 is a cross-sectional schematic view showing the structure
of such a dam.
In FIG. 58, 1 is the axis of rotation. The direction of rotation is
designated by arrow 1505. The inlet is at 1501, and the outlet is
at 1502. Dam 1503 extends radially inward from outer surface 1506.
Centrifugal force holds the liquid against the surface 1506. The
surface of the liquid is 1504. The innermost surface of the chamber
is 1507. With this configuration, liquid entering the chamber at
1501 is forced to traverse the chamber in the direction designated
by arrow 1508.
In chamber 1475, the direction of peripheral flow of the liquid
working fluid is not critical. In chamber 1461 this is also the
case. In chambers 1470 and 1469 the relative directions of flow of
liquid working fluid are important in establishing effective
operation as a countercurrent heat exchanger. For this reason, we
choose a direction convention. Direction "A" at an inlet means that
working fluid entering a chamber through that inlet flows away from
the viewer looking directly at the diagram. This means that it will
have gone into the diagram, around and come back to contact the
diagram and depart through the outlet. The letter "T" means that
the liquid moves towards the viewer, in the opposite sense to that
designated by the letter A. Flow of various working fluids is
designated by arrows in FIG. 57. Heat exchanger means 1571 of FIG.
56 has been omitted.
In connection with the system diagrammed in FIG. 56, it was
mentioned that instead of utilizing a pump P1413, it is also
feasible to break chamber 1438 at location 1404, and introduce into
the flow pattern at that location a lift tube compression assembly.
This has been done in FIG. 57. Chamber 1478 is the chamber in which
gaseous working fluid is driven off from the absorbent by heat from
heat source 1450, entering the device through thermodynamic
impedance Z1451. The combination of liquid and gas moves radially
inward through lift tube 1466, entering chamber 1475 at inlet 1484.
The liquid component of this working fluid proceeds peripherally
around chamber 1475 in accordance with the technique shown in FIG.
58. This liquid working fluid 1476 receives heat from heat source
1452 through thermodynamic impedance Z1453 driving off vapor 1477.
Heat sources 1450 and 1452 can be the same. Vapor-form working
fluid 1477 progresses radially inward through duct 1510, into
condensing chamber 1473. Within chamber 1473 it condenses, giving
up its heat of condensation through thermodynamic impedance Z1454
to some appropriate heat sink. Condensate accumulates against
outermost surface 1474 of chamber 1473, and drains therefrom into
conduit 1467. The surface of the condensate in conduit 1467 is
indicated at 1511. This condensate proceeds in the direction shown
by the arrows, through self-adjusting impedance control means 1481,
and continues therefrom to chamber 1458, in which it evaporates at
reduced pressure. Concentrated absorber leaves chamber 1475 through
outlet 1483, proceeding through conduit 1464 to enter chamber 1470.
Note the letter A at inlet 1487 to chamber 1470. This denotes that
the concentrated absorber, upon entering that chamber, proceeds
away from the viewer looking at FIG. 57. On entering chamber 1470,
hot concentrated absorber gives up heat through heat exchange means
1471, generally identified by distributed thermodynamic impedance
Z1455, which transfers heat from liquid in chamber 1470 to liquid
in chamber 1469. As the absorber progresses through chamber 1470,
it is exposed to vapor from evaporating liquid in evaporator 1458.
It absorbs this vapor, becoming progressively more dilute as it
does so, and giving up the heat released in the absorption process
through impedance Z1455 to heat the liquid absorber in chamber
1469, and drive therefrom vapor form working fluid through conduit
1468 into condensor 1473.
After it has reached the degree of dilution discussed in connection
with location 1406 in chamber 1435 of FIG. 56, the working fluid in
chamber 1470 proceeds radially outward through outlet 1488 to enter
chamber 1461 at inlet 1489. It then proceeds peripherally around
chamber 1461, absorbing vapor form working fluid from evaporating
liquid in evaporator 1458, and giving off the heat released in the
absorption process through impedance Z1456 to some suitable heat
sink. The heat of vaporization of liquid working fluid in
evaporator 1458 is supplied from some external source through a
total thermodynamic impedance Z1457. It is at this location that
useful cooling work is done.
The dilute absorbent from chamber 1461 proceeds through outlet 1490
to conduit 1463, and thence into chamber 1469 at inlet 1486. Note
the letter T at inlet 1486, denoting that liquid working fluid
flows towards the viewer looking at diagram 91. This is in the
opposite sense of motion to that occurring for liquid in chamber
1470. In this way, distributed thermodynamic impedance Z1455 acts
to provide the counter-current heat exchange required for operation
of the system in accordance with the principles set forth in
connection with diagram 56. After completing its peripheral travel
within chamber 1469, the relatively concentrated absorber leaves
chamber 1469 through outlet 1485, proceeding through conduit 1465
to re-enter the gas evolution chamber lift tube assembly at inlet
1479. It then proceeds peripherally around the device within
chamber 1478 to complete the cycle.
Absorber in chamber 1469 becomes progressively more concentrated as
it flows peripherally within the chamber. During this process of
concentration, the temperature at which it is in equilibrium with
vapor at the pressure in condensor 1473 increases, and its
temperature correspondingly increases. In this way, both the
absorption process in chamber 1470 and the evolution process in
chamber 1469 occur in a nearly reversible fashion.
Liquid in chamber 1469 and chamber 1477 is pressed upon by vapor in
equilibrium with the vapor in condensor 1473. This is at a
relatively high pressure, associated with the rejection of heat
through the impedance Z1454 during condensation of the vapor. In
evaporator 1458, vapor is at relatively low pressure. For this
reason, the liquid level 1514, in chamber 1470, is radially closer
inward to axis 1 than the liquid level 1513 in chamber 1469. The
difference between the radial positions of the two liquid surfaces
is designated 1512. In a similar fashion, the liquid surface 1516
of condensate evaporating in chamber 1458 is closer to axis 1 than
the liquid level 1511 in conduit 1467. The liquid surface in
chamber 1461 is at essentially the same radial distance from axis 1
as that in chamber 1470. Similarly, the liquid levels in chambers
1469 and 1475 are at essentially the same distance from axis of
rotation 1.
Conduit 1463 and conduit 1464 are also formed into rotary inertial
impedance control means to support a pressure difference associated
with the difference in the levels of liquids in chambers 1461,
1469, 1470 and 1475. Taken together with the chambers which they
interconnect, these conduits form a liquid trap type of impedance
control means, which has been discussed above in connection with
FIG. 26.
There is a significant difference between the problems of coupling
heat into a chamber such as 1475 in order to cause the evolution of
gaseous working fluid from liquid 1476, and those associated with
coupling heat out of liquid 1514 in chamber 1461 released by the
absorption of vapor. Similarly, the problem of transferring the
heat of absorption from chamber 1470 into chamber 1469 can be
solved by the use of a combination of the solutions to problems
used with chambers 1461 and 1475. In chamber 1475, heat from heat
source 1452 is coupled to outermost surface 1515 so as to heat the
portion of liquid 1476 which is radially furthest from the axis of
rotation 1. Thermal convection then causes this heated liquid to
progress radially inwardly. In this way, the bulk of the liquid is
easily heated by heat coupled to one surface to which it is
exposed. Evolution of vapor from the absorbent 1476 typically
results in an increase in its density. Thus, the material which has
haven up heat in the course of the evolution process also is
denser, and returns easily to receive additional heat through
surface 1515.
The foregoing processes, together, participate in forming
thermodynamic impedance Z1453. However, in chamber 1461, the
absorption of vapor produces heating in absorbent 1514 at a region
near its radially innermost surface 1516. This has two effects: the
heated material ordinarily is less dense because of thermal
expansion. Simultaneously, the dilution process typically serves to
decrease the density of the absorbent. These two effects combine to
cause the working fluid which has absorbed vapor to tend to remain
near the radially innermost surface 1516. For this reason, it is
desirable to provide heat transfer means within chamber 1461 by
means of which the thermodynamic impedance within the chamber can
be reduced. These are represented schematically by heat transfer
devices 1462. In a small rotary inertial device these can be
thermal conductors such as thermally conductive posts extending
radially outwardly to meet surface 1509 and transfer heat thereto.
These, together with the transfer properties within the liquid
itself, participate in forming the total thermodynamic impedance
Z1456, through which heat of absorption released within chamber
1461 is rejected to an environment.
Distributed thermodynamic impedance Z1455 is implemented by heat
exchange device 1471, including heat exchage posts 1482. Removal of
heat of absorption in chamber 1470 has essentially the same
problems associated with it as does removal of heat of absorption
in chamber 1461. For this reason, heat transfer means 1482 are
included within chamber 1470. For specificity, these are depicted
as being thermally conductive material. In FIG. 57, thermally
conductive and insulating materials are appropriately
cross-hatched.
The transfer of heat of absorption from chamber 1470 is implemented
by the thermally conductive rods 1482. When this heat is delivered
to surface 1518 of heat exchange device 1471, it is then available
for convective heating of liquid in chamber 1469. This convective
heating resembles that in chamber 1475, and for this reason does
not require special implementation by means of conductive devices
within the liquid itself.
In chamber 1458, provision is made for bleed of fluid through a
small port 1491. This port is located on the opposite side of a
radial dam near inlet 1517. During start-up, absorber may be
located in chamber 1458. The flow pattern established by the dam,
inlet 1517 on one side thereof, and outlet 1491 on the other side
thereof allows condensate from condenser 1473 entering at outlet
1517 to flush ahead of it the absorbing fluid chamber 1458 through
outlet 1491. This clears the chamber. The absorbant moves radially
outwardly into chamber 1461, where it mixes with other absorbent
fluid, and enters the correct absorbent fluid flow cycle.
The closed cycle device shown in FIG. 57, can be converted to a
device with a closed cycle for flow of absorbent fluid and an open
cycle for flow of absorbed gaseous working fluid, by breaking the
system open at locations 1519 and 1520. This removes from the
system chambers 1458 and 1473, and connecting conduit means 1467
therebetween.
Condensing and evaporation chambers 1473 and 1458 are depicted
diagrammatically. Their configuration can be modified to be
appropriate for the heat capacity required and to implement heat
exchange, both internally and externally, in order to obtain
desired values for thermodynamic impedances Z1454 and Z1457.
A device of the type shown in FIG. 57 can be built fairly simply by
dividing the structure axially into laminations, so that conduits
either are formed as holes through the laminations, or as slots cut
into their surfaces. In the same way, chambers can also be formed.
These laminae are then assembled and bonded to form the complete
unit. The technique is analagous to the techniques of assembly of
conduit and impedance control means from laminations with slots, as
is discussed herein below.
When no buffer gas is used in device 5000, the radial difference
1512 and the difference between radii to surfaces 1516 and 1511
support the pressure difference between evaporator 1458 and
condensor 1473. This is appropriate with some absorption cycles,
such as water and lithium bromide with water vapor, or water and
lithium iodide with water vapor. For ammonia and water systems, a
buffer gas is often convenient, with condensation and evaporation
determined by partial pressures of ammonia rather than total
pressures. A suitable "rectifier", not shown, as is well known for
ammonia and water systems, can be used. However, the countercurrent
absorption and reevolution process shown in FIGS. 56 and 57 is
particularly well suited to absorbtion cycles with a relatively
nonvolatile absorbent, such as a dissolved salt.
IMPEDANCE RELATIONSHIPS IN CASCADED SYSTEMS
Various forms of devices with different flow impedances can be
cascaded in series. For instance, if two rotary inertial
thermodynamic gaseous compressors with substantially different
thermodynamic impedances are cascaded, the result is a device which
has the capability of delivering a high forward pressure at low
flow and at high flow a relatively lower pressure, without having
the rapid dropoff in compression ordinarily associated with a
single high thermodynamic impedance device. Such arrangement is
shown schematically in FIG. 54. In FIG. 55, line segment 705
corresponds to operation of the high impedance compressor and low
impedance compressor in cascade. Line segment 706 corresponds to a
flow so large that the heat transfer within the high thermodynamic
impedance gaseous compressor is essentially negligible, and
essentially all of the compression arises from the performance of
the low impedance thermodynamic compressor. Region 707 designates,
generally, the changeover between operation of both systems
together in cascade and dependence upon the operation of the low
thermodynamic impedance compressor for compression. The system
referred to is shown schematically in FIG. 54, where Z.sub.T large
represents the large thermodynamic impedance gaseous compressor and
Z.sub.T small represents the low thermodynamic impedance gaseous
compressor. Flow is in the direction represented by arrows 730.
FLOW VELOCITY AND CONTROL
Thus far, in the discussion of gaseous working fluid rotary
inertial thermodynamic devices, it has been assumed that the
velocity of flow of the working fluid is relatively small compared
to the tangential velocity of the rotor at the point at which the
flow is measured. When the flow velocity for the working fluid
becomes an appreciable fraction, or even larger than, the
tangential velocity at any point in the rotor, then additional
effects appear which are associated with the coriolis forces. These
effects can be utilized to concentrate or distribute the regions in
which the gas has a range of temperatures or pressures.
FIG. 59 shows a portion of a rotor 1201 which is part of some
rotary inertial thermodynamic device. A conduit 1203-1204 is formed
in the rotor 1201. Gaseous working fluid is inlet to conduit
portion 1203 at 1208 and outlet from section 1204 at 1209. The
rotor 1201 rotates in the direction 1206 about the axis 1. Gaseous
working fluid progresses radially outward at a low velocity,
through conduit means 1203, passes around a bend 1210 and through a
DeLaval nozzle 1202. Upon leaving nozzle 1202 it has a high
velocity which is represented by the vector 1205. This velocity
vector is directed in such a way that its tangential component 1211
is exactly equal in magnitude and oppositely directed to the
tangential velocity 1207 of the rotor at that point. Thus, seen
from a non-rotating frame of reference, the gaseous working fluid
has left only a radial component 1212. Conduit 1204 is shaped so
that as the gas moves radially inward along the direction of its
radial component 1212, the conduit moves exactly the amount
necessary to make it lie directly in the path of the gas, so that
the gas experiences essentially no tangential momentum interaction
with the walls of the conduit. Since it experiences no appreciable
interaction with the walls, and since it does not experience any
change in velocity (except for some frictional effects) in going
from the point where it leaves nozzle 1202 to the end 1209 of
conduit segment 1204, it must have achieved upon exiting nozzle
1202 the properties which it has upon reaching point 1209. By
utilizing this contoured conduit, the properties which the working
fluid would ordinarily have only near the center can be extended to
a relatively large radial region. This is somewhat more difficult
to describe within the rotating frame of reference, but essentially
is equivalent to the balancing out of centrifugal and coriolis
forces with regard to the flow of gas in the contoured conduit.
If the pressure in the gas at the inlet to nozzle 1202 is high
enough, flow through the nozzle will be supersonic and there will
be a sharp drop in temperature of the gas at the nozzle exit. Since
the shape of the duct 1204 prevents expansion of the gas, it will
have the same low temperature all along duct 1204. This is a highly
advantageous feature in many applications.
It is not necessary for nozzle 1202 to produce supersonic flow; for
many situations it is sufficient that conduit 1204 simply be
appreciably smaller in cross-section than conduit 1203, so that the
velocity of a subsonic working fluid within it is appreciably
higher than it was in section 1203. With such an arrangement, the
temperature of the gas in section 1204 also will be relatively low,
and will remain substantially constant along the length of section
1204.
That temperature also can be made uniform along the length of a
section by gradually enlarging its cross section so that the
Bernouli effect changes the pressure in a way that tends to cancel
the centrifugally caused pressure change with radius. In FIG. 63
gas inlet at 4806 progresses radially outward in conduit 4801 in
direction 4805, inward in section 4802, 4804 and 4803, leaving at
4807. In region 4804, pressure increase associated with duct
cross-section increases balances decrease of pressure with radius,
holding the pressure essentially constant.
It is useful to bear in mind, also, in connection with the control
of velocity, that the velocity with which a working fluid passes
through a conduit affects both the mechanical impedance presented
to the working fluid by that conduit, and also the thermodynamic
impedance with repsect to the transfer of heat into and out of the
working fluid. The use of the Bernouli effect, that is, the use of
a change in cross-section of a conduit to influence the velocity
and pressure of a working fluid flowing therein, is also affected
by the location on the rotor. If the effect is used far out from
the axis, the working fluid will typically be at a substantially
higher pressure.
The use of the Coriolis and Bernouli effects allows the
distribution of the regions within which the heat transfer can be
accomplished, and in which the working fluid has specific
temperatures and pressures or ranges of temperatures and pressures.
In this way, it can be utilized to affect the design and
construction of impedance control means. It, in itself, can be
utilized for changing the effectiveness of impedance control means
by changing the velocities, pressures, and temperatures of working
fluids therein. These effects, in turn, are influenced by the
angular velocity with which the rotor is rotated. If the rotor is
rotated at a very high velocity, then the coupling between thermal
changes in density in the working fluid and mechanical work, in the
sense of motion within the rotor, become stronger, If the rotor is
rotated at very low angular velocities, this coupling between
motion and thermodynamic work becomes smaller.
The use of supersonic nozzles becomes relatively uninteresting when
the tangential velocity of the periphery of the rotor is below the
sonic velocity in the working fluid used within its conduits.
However, at relatively high tangential velocities, supersonic
nozzles can be utilized in connection with the Coriolis effect, in
the manner discussed in connection with FIG. 59. Moreover, the use
of a high molecular-weight gas (e.g., one of the "Freons") as the
working fluid can significantly reduce supersonic velocity at which
the use of supersonic nozzles becomes interesting. Utilization of
Coriolis, Bernouli and centrifugal effects together, is within the
scope of the stabilization techniques based upon impedance, that
is, slowly perturbed states of such systems will be stable if they
satisfy the impedance criteria given previously.
Because the Bernouli effect allows a control of the pressure and
temperature of a working fluid passing through a conduit, in
addition to affecting its velocity, utilization of the Bernouli
effect has as one of its consequences a change in the effective
interaction, between heat exchange means of any given temperature
and working fluid passing through a shaped conduit with a velocity
corresponding to a kinetic energy representing a significant
portion of its total energy. This, in turn, affects the
temperatures at which the thermal energy is accepted and rejected,
which has the effect of varying the thermodynamic impedance of the
gas dynamic process occurring within the rotor.
Consider, for example, the exchange of heat with the gas flowing in
conduit 1204, under the conditions described in connection with
FIG. 59, in which the component of velocity of the working fluid in
the radial direction is the only non-zero component seen in a
non-rotating frame of reference. In that case, the exchange of heat
occurs with a gas having the same properties as would be expected
relatively near the axis, but over an area ordinarily not
available. Or, suppose, at some intermediate point designated 1213
in FIG. 59, we were to introduce a somewhat smaller area ratio in
the shape of a convergent and divergent nozzle, so as to convert
the flow, once again, to subsonic velocities. Suddenly, the
pressure would increase, as would the temperature. By combinations
of these means, intricate rises and falls in temperature and
pressure can be achieved at various points in the rotor.
Similarly to a gas progressing radially inward, a gas moving
radially outward with a high velocity can be conducted within a
specially shaped conduit such that it does not experience
centrifugal and Coriolis forces until it is near the periphery of
the rotor. Such a specially shaped conduit 1216-1218 in a rotor
1221 is shown in FIG. 60. Rotor 1221 rotates in the direction
designated by arrow 1215 about the axis 1. A nozzle 1219
interconnects ducts 1216 and 1218. The tangential velocity of the
rotor in the vicinity of nozzle 1219 is designated by vector 1220.
Gaseous working fluid is inlet from some other part of the system,
not shown, at location 1222. It is outlet to some other part of the
system at location 1223. The velocity of the gas as it enters inlet
1222 is entirely radially directed. As the working fluid progresses
radially outward, the rotation of rotor 1221 brings each successive
portion of conduit 1216 into line with it, so that it is not
deflected by the walls. In the frame of reference of a stationary
observer, the behavior of the working fluid is as if it were
progressing through an essentially straight conduit. The working
fluid retains essentially the conditions which it had at inlet 1217
until it reaches the vicinity of nozzle 1219. Suddenly, its
temperature and pressure increase drastically as it is impacted
against the high pressure gases built up in conduit 1218, near its
outer end 1224. This ramming effect does not in any way require
that energy be delivered from the mechanism providing for the
rotation of the rotor. The angular momentum transferred to the gas
upon its sudden passage through nozzle 1219 is redelivered by the
gas again as it returns toward axis in the conduit 1218. Effects of
this type are most pronounced when the velocity of the gas and the
tangential velocity of the rotor are greater than the speed of
sound in the gas, because under such circumstances, no acoustic
wave propagates backwards from the pressure shock at nozzle 1219 to
change the properties of gaseous fluid at the entry 1222.
In addition to the extreme cases discussed in connection with FIGS.
59 and 60 of minimal interaction between the flowing gas and the
walls of curved conduits 1204 and 1216, respectively, the principle
involved of curving the conduit to use the Coriolis effects to
influence the behavior of the gas applies to a much wider range of
situations.
In FIG. 61 is illustrated a conduit similar to that shown in FIG.
60. This conduit has a shape which can be of interest in the case
of a relatively lower velocity flow of gaseous working fluid.
Conduit segments 1226 and 1227 both are curved to reduce the
interaction of working fluid with the walls. A bulge 1228 is
provided in the conduit. The bulge reduces the flow velocity and
converts kinetic energy of the gas into increases in both pressure
and temperature. For this reason, heat can be absorbed in region
1228 from a higher temperature heat source, without irreversible
thermodynamic losses, than would be the case if the conduit were of
the same cross-section throughout. The cross section of the conduit
is then again reduced in conduit segment 1227.
It will be seen from the examples given above that for systems with
high working fluid velocities, the various effects associated with
the interaction of pressure, temperature, velocity, and rotation,
should be treated in considerable detail. In particular, in cases
in which supersonic flows are expected to occur, considerable
attention should be paid to the stabilization of the shock waves
associated with the conversion between subsonic and supersonic, and
supersonic and subsonic, flows. By combining these effects, one
could, in principle, construct conduits which have properties not
unlike those associated with ram jets, in that a supersonic flow
would be converted to a subsonic flow at high temperature in order
to absorb heat from a high temperature heat source, and then be
reconverted to a supersonic flow again at relatively lower
temperature. Characterization of the behavior of the heat flows and
mechanical flows associated with such types of operation requires a
more detailed time-dependent analysis than has been presented so
far. However, the gross time independent features of steady state
operation should display the characteristic impedance properties
discussed already, in connection with systems involving lower
velocity flows.
THERMODYNAMIC TRANSFORMER
The considerations of thermodynamic impedance and efficiency can be
illustrated in a fairly simple example of a thermodynamic
transformer. There are many processes in which a mechanism by which
useful work is done has associated with it, intrinsically, a small
temperature difference. In order to do useful work, a large amount
of heat has to be transported through this temperature difference.
An excellent example of this is the purification of water by
evaporative transport. This can be utilized in desalination of sea
water, and also in the treatment of sewage. In both cases the
distilled water is a useful product, and the concentration of the
brine remaining, or of the sewage slurry remaining, requires the
performance of thermodynamic work. However, for a variety of
practical reasons, the maximum input temperature at which such
systems conventionally operate is approximately the boiling point
of water, about 100.degree. C. The minimum temperature at which
heat is rejected to the environment typically is approximately the
temperature of the inlet or outlet fluids, typically in the
neighborhood of 20.degree. C. For this reason, the absolute
thermodynamic efficiency of the entire process, viewed as a Carnot
cycle, is relatively low.
One useful way to raise the efficiency of the process would be to
allow the entire thermodynamic process to accept heat efficiently
from a higher temperature input. To this end, a rotary inertial
thermodynamic compressor can be utilized in a heat transport system
acting as a thermodynamic "transformer". In such a system, a small
amount of heat is utilized in a rotary inertial thermodynamic
gaseous compressor to actuate the transport of a large amount of
working fluid over a relatively low pressure differential. The
working fluid is raised to a sufficiently high pressure so that it
will condense slightly above the temperature required for input to
the small temperature difference thermodynamic process. The working
fluid, after condensation, passes through a suitable expansion
valve mechanism and is then evaporated at a slightly reduced
pressure, so that it evaporates slightly below the temperature at
which the thermodynamic process rejects heat. In this way, the
overall effect is to use a small amount of heat flowing through a
large temperature difference, (starting at the input to the gaseous
compressor), to move a large amount of heat associated with the
condensation and evaporation of the working fluid through the small
temperature difference appropriate to the performance of the
thermodynamic work required. This is the "transformer" action
referred to above.
FIG. 62 shows schematically a rotary inertial thermodynamic
transformer 1249 of the type described above. The transformer 1249
includes a rotary inertial thermodynamic gaseous compressor 1250
actuated by a heat source 1256 through a thermodynamic impedance
Z1258. Working fluid is outlet from the compressor 1250, in the
direction of arrow 1251, to a condenser 1252. From condenser the
1252 heat of condensation is delivered through two impedances,
Z1259 which could be a very small load or zero load, (i.e., high or
infinite impedance) which is presumed to be heat rejected from the
system entirely; and Z1260, which delivers the heat to a load 1261
requiring a small temperature difference. The load 1261 can be, for
example, the evaporator and condenser of a conventional "flash"
evaporation desalination plant. Outlet of heat from load 1261 is
through two impedances. One of them is an impedance by which heat
can be rejected from the system Z1263. The other is for the
rejection of heat to the evaporator 1254, through an impedance
Z1262.
Liquid working fluid flows from condenser 1252 through flow control
means 1253 into evaporator 1254. Within the evaporator it
evaporates, absorbing heat from the load 1261. Vapor form working
fluid proceeds in the direction shown by arrow 1255 and reenters
compressor 1250. For many applications, for example, desalination
of water or purification of sewage, it would be desirable to make
Z1259 an essentially negligible loss of thermal energy, and use
Z1263 as a heat source for the operation of a cascaded evaporative
transport or other thermal purification plant. Alternatively, the
process of load 1261 can represent evaporation across a
single-stage still, utilizing the impedance conversion in the
system as a whole to allow the process to accept heat efficiently
from a high temperature heat source.
Preferably, the condenser 1252 and evaporator 1254 are stationary.
1265 represents some thermodynamic process running on rejected
thermal energy, rejected from the process of load 1261 through an
impedance Z1263. For example, if load 1261 is the first stage of an
evaporative transport purification plant, subsequent stages might
be operated from the waste heat therefrom. In that case, 1265 would
denote the thermodynamic process of the evaporative purification
plant following the first stage. Such a plant, by the laws of
thermodynamics, must reject heat to its environment, and the
impedance through which it is rejected is designated Z1264.
Stabilization of the operation of a system of this type depends
upon making the flow through the total system have a positive
impedance slope. This can be achieved by manipulation of impedance
Z1258 and, in general, would occur if a high-impedance heat source
were used. Most of the heat sources of interest for actuating such
treatment systems have the characteristic high impedance desired.
These include combustion of fuel, nuclear energy sources, and solar
energy sources.
For purposes of comparison, the maximum Carnot cycle efficiency
which can be obtained, accepting heat at 100.degree. C., and
rejecting it at 20.degree. C., is roughly 22 percent. The maximum
Carnot cycle efficiency which can be achieved in a rotary gaseous
compressor is appreciably greater than that. This allows a
substantial increase in overall operating efficiency. A second
characteristic of a transformer system of this type is that it does
not require the utilization of a large number of cascaded
evaporation stages to achieve its high efficiency. Therefore, the
way in which efficiency is related to size of plant is not the same
as it is for a conventional cascaded flash evaporation plant. A
unit of this type can remain efficient even in relatively small
sizes, utilizing an impedance matching system of this type for
accepting heat from a high impedance source, efficiently for
operating a low impedance thermodynamic load. With the transformer
of the present invention, one can achieve a relatively quite large
heat pumping ratio, that is, the amount of heat transported between
condensor 1252 and evapoator 1254 can be many times the amount of
heat transported from heat source 1256 to the external heat
rejection point through impedances Z1259 and Z1263.
In the case of purification of salt water or sewage, the external
heat sink can be the effluent from the plant, be it the purified
material or the rejected concentrated impurities; that is, such
materials can have somewhat higher temperatures than those with
which they entered the plant, the heat is rejected by this means
and no special heat sink is required.
There are many low-grade heat processes in which this transformer
can be used. For example, the concentration of alcohol,
purification of water by freezing and/or clathrating, and the
operation of distillation plants and related vapor transport
purification processes. These processes are amenable to this type
of thermodynamic impedance matching, which would allow them to be
operated with higher efficiency from heat sources having
characteristically high temperatures and thermodynamic
impedances.
A thermodynamic transformer of the type shown in FIG. 62 is
particularly attractive in the use of freezing or clathrate
formation as a purification technique. It is a technique which
requires a relatively small temperature difference, but which
requires that temperature difference in a temperature domain not
lending itself to operation directly in cascade form from a heat
source. For this reason, fairly intricate systems typically are
required to provide efficient operation in an ice type of water
purification plant. Also, processes involving the utilization of
differential solubility of one material in another for purification
typically can benefit from the availability of a large volume of
heat flowing across a small temperature differential.
A transformer system of the type shown in FIG. 62 can also be used
advantageously for the heating and cooling of large buildings and
other types of installations utilizing the external environment as
a heat source and/or heat sink. When used for such an application,
a system of this type offers great flexibility in that the heat
pumping ratio, defined as the amount of heat transported divided by
the amount of heat drawn from the heat source, can be varied to
take advantage of the operating conditions so as to always operate
with high thermodynamic efficiency. Thus, if there is a small
difference between the external environmental temperature and the
desired temperature within an enclosure, the heat pumping ratio can
be made very large. This allows a considerable saving in operating
energy. This kind of flexibility is relatively difficult to obtain
using existing absorption cycle systems or steam ejector type of
systems. Very high heat pumping ratios are theoretically feasible.
Moreover, high thermodynamic efficiency could be maintained over a
relatively wide range of heat pumping ratios.
LOW LOSS REFRIGERATOR
By utilizing a gaseous compressor and a gaseous expansion type
refrigerator, one operating the other and coupled together
thermodynamically, with the other it is possible to achieve a
system which has a relatively low loss, so as to maintain an
isolated region at relatively high pressure while permitting
working fluid to flow into it and out from it. FIG. 64 shows such a
system. In FIG. 64 the axis of rotation is 1. Working fluid enters
at inlet 1270, passes through compressor 1272 into the
high-pressure region 1274, thence through refrigeration-type heat
pump 1273, and out at the outlet 1271. The temperature differences
for operation of both the compressor 1272 and the refrigerator 1273
are maintained by the heat flow from heat source 1275 through
impedance Z1276 into the devices, and out therefrom to a heat sink
in the external environment through impedance Z1277. Heat flow
between devices 1273 and 1272 is indicated by arrows 1278 abd 1279.
Because of the thermodynamic reversibility of the gaseous
compression and refrigeration processes, device 4810 can
equivalently be thought of as two gaseous compressors back to back,
with the high pressure region 1274 between them. What is
illustrated is the simplest case, a single stage. By utilizing a
large number of stages in cascade, with half the stages operating
in the forward direction, followed by a high pressure region,
followed by the other half of the stages operating in the reverse
direction, it is possible to achieve in the high-pressure region
extremely high internal pressures and yet have relatively free flow
of working fluid into and out of that region.
Such a process is interesting for use in chemical reactions, for
example, for the production of ammonia, in which the utilization of
a high pressure permits the equilibrium point for the chemical
reaction to be appreciably shifted in the direction of the desired
product. It is important, for an application of this type, that the
compression and expansion portions of the system be in intimate
thermal contact with each other. Thermal losses, in transferring
heat from one to the other, give rise to effective pressure losses
which must be overcome in maintaining the pressure. The source of
energy for overcoming these losses is the flow of heat from the
heat source to some heat sink. It is not necessary for the heat
sink to be external to the device, provided that there is some way
for working fluid to carry off that heat, which, by the laws of
thermodynamics, must be rejected to the environment.
COMPRESSOR STRUCTURES
FIGS. 65 and 66 show a desirable form of construction for rotary
inertial thermodynamic gaseous compressors. FIG. 65 is an exploded
view of the compressor. In FIG. 65, 920 and 922 are impermeable
plates made, for instance, of a suitably thermo-conductive
material, such as aluminum or some other metal, or beryllium oxide.
Core 921 is a circular disc made of a thermally insulating
material, for example, a foamed epoxy resin formed as a syntactic
foam, a polystyrene foam, or any other suitable insulating
material. Into this material are formed slots, 923, 924 (FIG. 66)
on opposite faces of the disc. Only a small number of slots are
shown in FIG. 66, for the sake of simplicity. Actually the slots
extend completely around the periphery of the disc 921.
Holes 926, 927, 928, 929, etc., are provided in the disc 921 at the
ends of the slots 923 and 924. This connects one end of a slot 923
with one end of a slot 924 on the opposite side, and the other end
of slot 924 with one end of the next upper slot 923, and so forth
around the disc 921. Face plates 920 and 922 are bonded to core
921, thereby closing the open faces of the slots formed therein and
forming closed conduits suitable for carrying working fluid in a
spiral path like that illustrated in FIGS. 12 and 13. Selected
slots extend radially inward and connect with apertures in face
plates 920 and 922 to serve as inlets and outlets. In FIG. 65, the
aperture is designated 925 and the radially extended slots
connecting thereto is designated 930. Construction in this form has
several advantages. First, plates 920 and 922 can be formed by
simple stamping. Core 921 carries essentially all of the shaped
structure defining the flow conduits. This piece can be formed
simply by molding. With this construction technique, the number of
parts used to form the assembled rotary inertial thermodynamic
gaseous compressor can be essentially independent of the complexity
of the flow paths for the working fluid within. The device can have
many parallel branches, and can have many stages in each branch.
The conduits can be made shallower and deeper, they can be curved,
they can have recesses left within them to accept heat exchange
means, magnetic drag means, electromagnetic heat absorption means,
radioisotope heat production means or other appropriate mechanisms
or structures suitable for the stable operation of the rotary
inertial thermodynamic gaseous compressor.
In a rotary inertial thermodynamic gaseous compressor formed of
three layers (as shown in FIGS. 65 and 66) the two lids can be
utilized as heat exchange surfaces, with one maintained at a
relatively high temperature from which the internal processes
absorb heat, and the other maintained at a relatively low
temperature to which the internal processes reject heat, in the
manner illustrated in FIGS. 12 and 13. In this way, thermodynamic
connections for heat transfer with the various impedance control
means within the conduits within such an assembly become relatively
simple. A particularly desirable form of impedance control means is
a set of finely spaced fins which desirably are formed as part of
the lids. For example, fins 1552 on lid 920 fit into the ducts when
the device is assembled. External fins 1553 can be formed in the
same way, ina single process if desired. The sealing properties and
most of its structural properties are determined by the assembly of
the three layers 920, 921 and 922. The shaft passes through a hole
931 in the assembled device. Alternatively, the device can be
supported by hubs, or by assembly to some other rotating member.
Optionally, the device can be sealed using a conventional type of
can seal 1550 near the periphery, formed with extension 1550 of
plate 920.
In FIGS. 67 and 68 is shown an alternative form of construction for
a gaseous compressor utilizing laminations assembled to each other
to form ducts. In these FIGS. 1001 designates a molded body of
insulating material bearing grooves 1009 which, when covered by a
lid 1008, form conduits. In FIG. 67, these conduits, sections of
which are 1002 and 1003, are seen to contain appropriate impedance
control means 1004, 1005 and 1007 (e.g. heat exchangers as shown in
FIGS. 39 and 40). A central hole for a shaft is designated 1006.
Selected portions of the lid 1008 or core 1001 can be made
thermally conductive to facilitate transfer of heat into or out of
impedance control means, as appropriate.
FIG. 69 shows a preferred gaseous compressor construction utilizing
lamination techniques. Laminates in the form of discs 510, 511,
512, 513, 514, 517, 518, 519, 520, 521 and 522, together with a
core 516, form the conduits for conveying working fluid, and also
the impedance control means operative therein. This is illustrated
in section 70--70, (FIG. 70) in which can be seen holes 532 and 533
through core 516 for conveying working fluid into and out of
impedance control means 520 and 531. The impedance control means is
constructed by forming elongated, tapered slots in one half of the
discs, and forming half-moon-shaped slots in the other half of the
discs. Holes 532 and 533 are formed in the core 516. The discs are
assembled with discs having half-moon slots alternating with those
having elongated slots, thus forming thin flow passageways through
which the working fluid can flow.
FIG. 70 shows that the slots are canted at an angle with respect to
radii of the disc, so that when two stacks of the discs are formed,
one group of slots "stage" or move over by one increment, and the
facing slots stage over by the remaining portion of the increment
necessary to complete an entire step, so that the fluid flows first
through one conduit, through core 516, then through the conduit in
the opposite stack, through the core again, and then on to the next
stage of the conduits in the first stack. In this way, a large
number of stages can be cascaded in a manner analagous to that
utilized with a molded core and discussed in connection with FIGS.
65 and 66.
In a similar manner, laminations 526 can be seen in FIG. 71 to form
an external set of heat exchange fins. Alternate ones of these fins
have apertures extending out from the center, or extending in from
the edge. This leaves a set of blades of the type 540, and a set of
apertures of the type 539, such that it is possible for air to
circulate through the stack. Dotted lines 538 and 537 denote the
hidden edges of a set of apertures hidden behind blade 1300. In
this way, stack 536 becomes a set of heat exchange fins for
coupling heat to the external environment, in this case for
rejection of waste heat thereto. Apertures 544 are inlets within
intake manifold 508, allowing working fluid to flow into the
multiple branches of the parallel-branched gaseous compressor shown
in FIG. 69.
Referring again to FIG. 69, 542 is a shaft. Bearings are at 507 and
524, rotary gas seals are at 501 and 525. Sheaves 503 and 505, belt
504, and motor 506, serve to rotate the rotary device. Outlet
manifold 523 is illustrated diagrammatically in FIG. 72. In FIG.
72, 1301 is the wall of the manifold, 1302 denotes generically the
outlet ports from the various branches of the parallel-branch
compressor. 1303 denotes a few of the flap valves utilized to make
the operation of this gaseous compressor unconditionally
stable.
In FIG. 69, 527 is an annular baffle, utilized in conjunction with
burner 528 with inlet 529 to provide heating for the gaseous
compressor. An assembly of this type can be formed from simple
stampings. The various laminations can be joined to each other
using adhesives or other techniques. For example, if the
laminations are formed from titanium, or a number of other suitable
materials, they can be diffusion bonded into a hermetically sealed
stack. In order to avoid the possibility of leakage at a large
number of external seals, it is possible to use a thin outer wall
1304 formed by bringing lamination 510 past the thickness of the
compressor to make a single seal, e.g. a conventional type of can
seal, at location 1305. Although this is shown at just one location
it is presumed to extend entirely around the periphery of the
gaseous compressor device, and form a can having a single seal at
the periphery. In this way, the reliability of the sealing of such
a device can be greatly improved, if desired. Inlet to the entire
device is at 1306. Outlet from the entire device is at 1307. Flow
is in the direction designated by arrow 1308. There are many ways
in which devices of this type can be fabricated. For instance, when
a lid is formed it can be formed bearing the necessary heat
exchange devices upon it, in a single operation. Such variations of
that type are within the scope of the analytic technique and
principle of impedance control for stabilization.
WORKING FLUIDS
It is to be understood that the working fluid utilized in a rotary
inertial thermodynamic device does not have to be of a single type,
such as a gas or a liquid. It is possible to utilize the
thermodynamic properties of aerosols, so as to delimit in a
specified way the magnitude and nature of the temperature
dependance upon pressure during compression and during
expansion.
INTERNAL REACTION FORCES FOR ROTARY DRIVE
In my copending application, I have described various ways in which
a closed loop rotary inertial thermodynamic device can be caused to
provide its own rotation. Quite generally, a rotary inertial
thermodynamic compressor can be used to actuate a relative motion
within a rotating device, which relative motion can be caused to
rotate, or contribute to rotation of, the rotating device.
One way to do this is to allow a moving working fluid within the
rotating device to react against a stationary piece, held
stationary by some suitable means, such as a magnet, or gravity.
The stationary piece does not have to be balanced, and a large
amount of wear can be tolerated in its support bearing. In FIG. 74
is diagrammed such means for rotating a device. 1731 is any
suitable rotary inertial thermodynamic compressor, in this case a
gaseous device with one stage. 1730 denotes generally a rotary
drive device, including chamber 1737, inlet tube 1732, jet nozzle
1733, stationary magnetic material bar 1735 mounted to rotate on
shaft segment 1736 by means of bearing 1738, outlet 1739, and
magnet 1734. Bar 1735 is kept from rotating by magnet 1734.
Compressor 1731 is assumed connected to a larger system, not
shown.
High pressure gaseous form working fluid is bled from compressor
1731 at location 1741, through conduit 1732, to produce a stream of
high speed jet of gas flowing from nozzle 1733 into chamber 1737.
Nozzle 1733 is directed tangentially, backwards from the direction
of flow. The reaction force from the gas drives the nozzle
backwards, rotating the rotary device. The equal and opposite
reaction occurs when the swirling gas in chamber 1737 strikes
stationary bar 1735, which in turn transmits this reaction force to
magnet 1734, thus removing the opposed reaction force from the
rotary device. Thus, the reaction force against jet nozzle 1733 has
no counterbalancing force within the rotary device, and so produces
a net torque to rotate it. Note that even relatively severe wear of
bearing 1738 has little effect on performance of the rotary drive
device. The stationary piece can be extended, with magnets placed
symmetrically about it, so that essentially no component of the
magnetic force appears as a load on the bearing. Alternatively, in
chamber 1737 can be located a balanced magnetic rotor, spun in the
reverse sense to the direction of rotation of the larger rotary
device, and serving as the rotor of an electric generator, whose
stator is appropriately placed outside chamber 1737. Electric power
production in the generator gives rise to a magnetic drag on the
magnetic rotor, consuming the reaction forces from the gas whirling
in chamber 1737, and thus serving the same purpose as bar 1735 with
magnet 1734.
From rotary drive 1730 and modification for use as a generator, one
can proceed by simple steps to the incorporation of elaborate
mechanical devices within the rotary device, operated with working
fluid compressed by a rotary inertial thermodynamic compressor. As
long as coupling is provided to allow reaction forces to leave the
rotating device, a driving effect can be achieved. Of course, the
use of working fluid for such purposes must be included in
determining the impedance into which the compressor will have to
deliver working fluid, and, consequently, the mechanical and
thermodynamic impedances throughout the compressor. The ability to
use a stationary "rotor" in a turbine or similar device operating
within a rotary device can greatly simplify the stationary "rotor".
For example, it can be unbalanced. Also, the life of bearings
inside the rotary device, used to support stationary parts within
it, can easily be made quite long. Thus, their relative
inaccessability, compared to external bearings, is not a severe
handicap. The definition of failure of such bearings is also often
much less stringent, because of the relative absence of
wear-induced wobble.
COMPRESSOR WITH SECONDARY PUMP
A secondary pump means cam be used to compress a working fluid
which does not necessarily condense within the rotary inertial
device. In FIG. 73 is illustrated such a rotary inertial
thermodynamic device, 1720. In device 1720, 1700 is the inlet, 1714
the outlet, 1704 denotes generally a secondary pump means actuated
by rotary inertial compressor 1725, in this example including
nozzle 1702 and diffuser 1703; condensor 1705, evaporator 1708,
rotary inertial trap 1707, heat source 1711. Gaseous working fluid
A enters at 1700 in direction of arrow 1701. It is compressed in
secondary pump 1704, in which it mixes with vapor form working
fluid B, which enter condensor 1705 in the direction of arrow 1715.
In condensor 1705, vapor B condenses, giving up its heat of
condensation through thermodynamic impedance 1712 to a heat sink
not shown, flows radially outward into trap 1707, filling it to
some radius 1706. Liquid B proceeds in direction of arrow 1719,
entering chamber 1708 to form annular pool 1709. Liquid B is
vaporized by heat from heat source 1711 through impedance Z1710,
returning through conduit 1723 to actuate secondary pump means
1704. Difference in radial location 1722 of liquid surfaces 1718
and 1706 is associated with operation of device 1721 as a
compressor, as in FIG. 26. Uncondensed working fluid A leaves
device 1720 at 1714 in direction of arrow 1713. Devices of this
type can be combined, with a cooling device with shared condensors,
as shown in my copending application. Used separately, a device
1720, with suitably designed secondary pump means, can be used as a
vacuum pump, compressor, etc. Inlet 1700 and outlet 1714, of
course, do not have to be on axis 1. Stable operation of a device
of this type depends on stable operation of its rotary inertial
thermodynamic portion, and thus on mechanical and thermodynamic
impedances of the device and the total system of which it is a
part.
As can be seen from FIG. 26, it is important in the design of heat
exchange chambers to consider the tendency of liquid to move
radially outward. For this reason, it is highly desirable that
ports for gas inlet and outlet be located radially inward from
those through which liquid passes. This same design consideration
applies to the details of heat exchange means and, more generally,
impedance control means. Following this design practice avoids
unwanted backpressures and thermodynamic inversibilities associated
with forcing a gas to bubble radially inward through a liquid.
GENERAL ANALYTICAL MODEL OF SYSTEM
FIG. 75 shows schematically the analytic structure of a rotary
inertial thermodynamic system, identified by its acronym "RITS" in
FIG. 75. The figure is depicted as including a rotary inertial
thermodynamic device 1350, (designated "RITD") having within its
internal mechanical impedances designated generally by [Z.sub.m
INT] to denote that there can be a plurality of such impedances,
and internal thermodynamic impedances designated [Z.sub.T INT] and
a geometric configuration represented by G. Input to this system is
an angular velodity designated W, and operating in conjunction
therewith are mechanical impedances external to the device and
thermodynamic impedances external to the device, designated
generically Z.sub.M EXT. and Z.sub.T EXT., respectively. The
performance of the rotary inertial thermodynamic device is affected
by all of these impedances. The conditions set forth in this patent
application are appropriate for the analysis of all rotary inertial
thermodynamic systems of this general form. A number of selected
examples have been given in the disclosure in order to show the
generality of the method of analysis, and illustrate ways in which
they can be applied in specific cases. The applications in these
cases serve also to illustrate the great advantages which rotary
inertial thermodynamic systems possess for a wide variety of
applications of practical importance.
It is to be understood that although specific details have been
described in the context of examples, the various features
disclosed herein can be used in combination with each other and can
be extended in ways which will be apparent to workers in the field,
without departing from the technique of stabilization of flow of
working fluid within a rotary inertial thermodynamic device by
controlling its internal and external mechanical and thermodynamic
impedances.
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